Well, yes, but a few things need to be understood. In a high stress/high adrenaline situation, the higher functions of your brain will simply shut down, leaving only the more survival-orientated functions to be utilised. The functions lost include the ability to form complex sentences, and perform complicated techniques (without a huge amount of repetitive training with the correct approach). Another thing it will do is shut down your conscious minds ability to critique and make decisions the way you can do right now (as you read this).
A few threads recently have given very good examples of this, one (The Destroyer Style) speaks very strongly to this at the end. The stories of a number of incidents where the ability to consciously make decisions cost people's lives, as they followed procedure designed to make cleanup in a shooting gallery easier.
So if you think you will be able to consciously "choose" what techniques/tactics you will employ, or whether your BJJ is the best, or Tae Kwon Do, or Aikido, realise that that very decision-making ability will be one of the first things you will lose. That leaves us wondering, in a lot of cases, what will come out? If we train in a variety of arts, each with their own different power source, movement style, strategic base, tactical approach, and more, which will come out? Well, that will be the one that you unconsciously beileve is the most powerful.
I'll say that again. It will be the one that you unconsciously believe will be the most powerful.
And that will have nothing to do with what you rationally, consciously, logically think or believe it is. It is, instead, whichever your unconscious believes. Now, the unconscious mind is an interesting place. It is the storage place for every experience you have ever had, as well as where your beliefs, values, and behaviours come from (you act the way you do because of your unconscious mind, not due to any conscious decision. This is what we refer to as our "personalities"). By and large, the values and beliefs that determine our behaviours are pretty much set by the time we are 7 years old, with a bit of tweaking until we are about 15 or 16. The only ways to change this after that are traumatic experiences (hence the term "life-changing" experience), or therapy (usually quite intense). The only other variant to this is if there was no previous value installed, in other words, if you have no experience at something, and no experience to relate it to, then a new value and belief can be created from a new experience.
Training can be traumatic, but really falls under the category here of "therapy". It is therapy because it is an undertaking to alter your behaviours, which is achieved by giving new experiences to "replace" previous beliefs and values, which then give you your new behaviours. But the experience needs to be powerful enough to replace any previously existing beliefs. I'll explain.
Say you saw a movie when you were young. Let's call it The Karate Kid... In this (hypothetical!) movie, there was a protagonist who has distinct disadvantages, he is smaller than the other kids, has less ability, and is constantly bullied and beat up. He discovers a local martial art master, who teaches him (in a rather unorthodox, and honestly ineffective way, only giving physical movements without the necessary context and appropriate mindset for the actions to be utilised... but I digress...) the skills of a particular martial art. Using this new skill, he takes on the bullies, and wins the girl, a trophy, and his self respect. And he did this using an exotic-style technique (a rather telegraphed action which announces it's intention ["I'm going to kick!"]) from this martial art.
Now let's say that you saw this film when you were quite young. In fact, this was your first real experience seeing martial arts (and relating what they are, in terms of handling violence and life's obstacles). Now the only experience you have in terms of martial arts are this film. So, with your unconscious mind being unable to differentiate between fantasy and reality, the only reference it has to create a belief about martial arts, and to give them a value, is this piece of hollywood. The belief could go a number of ways, but we'll take it as a high value experience, which means that your belief about martial arts are that they look like what you saw in the movie (they all look like karate, lot's of striking and kicking, little grappling, forward facing aggressive postures etc), this is what works, this is what is powerful, and it is the exotic, different techniques (like the single-legged crane-kick) that are needed to be successful (as a side note, if you see kids play fighting, they will often go to these "movie" poses, as they are percieved to be more powerful. They will almost never go to a boxer's pose, nor an Aikido Hanmi, nor any other. What is in the movie's are powerful...).
So a few years later, you take up a martial art. You may take up Tae Kwon Do, or Karate, as that looks like what you personally believe to be powerful... but you may not. You may take up something entirely different, such as Aikido, WIng Chun, or Ninjutsu, for conscious belief reasons. But if the training is not sufficiently designed to replace your previous beliefs, then you may find that, despite a number of years training in a completely different type of system to karate (let's say Aikido, yeah?), when you are put in a high stress/high adrenaline situation you are likely to respond with a version of the karate your unconscious mind believes to be more powerful. The conscious mind really doesn't enter into it.
But if the training is done well, or is geared in such a way to convince you that it is more powerful than the karate you have seen or trained in, then a new belief takes the place of the old one, giving new values (Aikido I have trained in is more powerful that karate from movies), and that changes your behaviours (Aikido comes out, rather than karate). This could happen a number of ways, most often the art being "proved" to you, being on the recieving end can do that.
Just remember that if you have trained in both systems over time, your unconscious mind will choose whatever it believes is the best of the different options, not switch between them. So if you trained karate when you were 6 through to 9, and had it's power instilled in you, and Aikido from 22 through to 29, but never had it sufficiently demonstrated to you that Aikido was stronger, you will probably still find the karate making an appearance under stress.
Hopefully that helps you understand the psychology behind this (and the training ideas). This is why cross-training and taking bits of this and bits of that because they "seem to work" is really actually to be discouraged, unless it is able to be congruently adapted to an existing base. Otherwise you are honestly wasting a lot of your time...