No, that has nothing to do with that. We're talking WAY different scales here.

For life to develop you do need some stability of course, I mean, a supernova going off next door won't be helpful. :-) But for life we're talking about the local environment. Things like: how far is the nearest star? What is the chance of trouble nearby?

As for a crowded set of Galaxies, the chance of galaxy collisions is indeed higher, but when galaxies collide, in general, stars do not collide. You do get a BUNCH of new star formation, but locally things can still be stable. Looking at individual galaxies within the Virgo cluster we're not seeing much different structures like what we see in our own Milky Way...

There are vast voids in space. There are few to no galaxies in these areas, and they take up about 80% of the universe. Anywhere not a void is actually relatively boisterous compared to the average.

https://en.wikipedia.org/wiki/Void_(astronomy)