Not necessarily. I know five judo dojos in my area. Two are affiliated with USJA, and one with USA Judo. Of the remaining two, one is independent and the other is affiliated with IFJA (International Freestyle Judo Alliance) - an association not recognized by the IJF. So we're 3 for 5 in my area for Judo.
I was involved in a pretty heated debate on Reddit about this: the importance of being affiliated with an association or federation. Some believe that it's important, others don't.
I'm of the mind that it is. However, this doesn't just pertain to martial arts. For example, if you look at the so-called "pimp preachers" - like Creflo Dollar, Joel Olsteen, and the late Eddie Long - they tend to be Baptist, non-denominational, or any other denomination that has a congregational polity (as opposed to an episcopal polity). This doesn't mean that those denominations of Christianity are bad. But what it does mean is that is that the pastors of these churches have no bishop, elder, archbishop, presiding bishop, metropolitan, patriarch, pope, or whatever above them to answer to. Hence, pimp preachers have the freedom to do pimp preacher things unchecked.
That's why I check for associations when selecting a dojo.