Is it necessary to become physically stronger and more fit in order to utilize Systema methods for self protection? No -- it is your skill that ismost important...but you would most probably see an improvement in 'fitness' as a by product of the training.
Some of the exercises, though; are abit deceptive. It would seem that beathing pushups are possibly a strength developer..but they do more -- stressing the tendons, emphasising a shoulder rotational movement for going up and down aids proper punching form, it trains the will and breathing and helps one to lose the tension in the body that we often store up during the day -- allowing for a more delicate kinesic awareness of the movement of the body. Simple push up..it does alot.
On a larger view -- since 'the body' is the vehicle for one to express movement, a more fit vehicle will perform more effectively when called upon. Just depends on what you are focusing on when you are discussing fitness. When I began in Systema, I had come from over 30 years of the oriental/traditional western/eclectic schools of training. Weight training, for example; was a very strong point with me. Aerobics not so much -- for after all, I was training to hit hard and a real fight is not a marathon event, right?
(Wrong -- aerobic fitness is important..in 'the real', you may not go very long but you go really hard, and it taxes the breathing -- remember, this is my pre-systema training/fighting experience I am talking about above).
So, I came to systema as a relatively 'strong' guy -- and I looked the part of the m.a. fighter. The problem was...my 'strong' weight trained body had a constant high level of tension in the muscles -- a high level of 'tonus' -- as I still retained flexability, having trained to keep it. I found that this tonus was preventing me from developing the required awareness of my bodys free movement to make good progress in The System...so, as hard as it was to walk away from the iron, I wanted to 'do the work' so badly -- and I left the weight room alone for the better part of 2 years. I concentrated on the strange yet simple(?) exercises that Vlad was passing along. In that 2 years, my body awareness blossomed and grew considerably. I lost the constant tonus...and regained free movement. since then, I have returned to the iron, but train differently. Physical size and the weight pressed is not important now, the movement made 'under load' is...feeling it, varying it. I have also become a devotee to the use of the kettlebell and clubbell - finding them excellent additions to my overall fitness regimen.
I also run as well as my poor 50 year old knees permit -- for about 25 or 30 mins./3 or more times a week. Usually after work -- at about 1 in the morning, when the city streets have less traffic.
As I write this, it seems like the reader might think I do nothing but train. Far from it. I have just managed to fit it into my day comfortably -- it really is not so hard to do. Just substitute the training for some time in front of the TV -- hardly a sacrafice.
When do I find time to actually train Systema? Well, I teach twice a week and train also twice a week for myself...but that is not the limit to the actual training. Just moving throughout the day, in a 'proper' way, provides me with a great workout also. Opening doors are now done in a 'deflection' manner, moving through a crowd provides a lesson in movement every time I do so, as I find many ways to express what I have learned in the most mundane of lifes tasks.
Thanks to Vlad -- 'movement' is simply 'movement' now...'breathing' training is simply how I breath now, I retain a certain understanding of 'form' no matter what i seem to be doing....and I have (thankfully and finally) learned that 'relaxation' is a constant and normal way to 'be' -- all the time. So, in a way -- I am always training Systema, as I apply it in my daily life.
OK - did it again...a long post.
To sum it up, as above; since 'the body' is our vehicle for expressing Systema -- the more efficient the vehicle, the better the System's expression in your life...and the better you can respond 'when things are not good' and you might have to call upon that vehicle for some form of self protection or the protection of another.