Sure it could be done, but why? There's always going to be a "best" setup for raiding.
It can be done without the best weapons, but who wants to "three, maybe four phase" the boss at GoS when you can do it in two? The challenge? That doesn't seem to be the "point" you're trying to make.
Now, if you were talking about putting a team together with all blue weapons and armor to go into Crucible, that'd be different.
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The point I’m trying to make is that friends of mine are saying you have to use weapons with specific perks in order to clear encounters. I’m saying it can be done with whatever weapons you want to pull from collections.
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You're absolutely right. You can grab any sniper rifle to do damage, but some do a much better job than others.
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It's all dependant on the encounter. There are certain perks (mostly on Exotics) that will be more helpful than others in damaging a boss.