You are right that you should be able to pick that up.
But anyway the ammo and the guns should normally be transferred to base (maybe sold already and available over the buy/sell button) even if you do not pick anything up on the battlefield.
Only problem occurs when you do not have enough ammo for your own guns or want to use the gun of a dead alien (that's your problem, right?).
Before the workers can produce something the scientists must find a way to reproduce the technology (a prototype and schematics) which is not possible for some guns right now... but I guess we already got each other right.
If you cannot research/produce it anytime (as I suppose it is planned for now) there is no need for a grayed out note in the research button. The research report of the weapons point out everything necessary to know.
Although you might find it a bit too long to read completely - as I also did.
I messed plasma guns with particle beam guns, sorry about that. You cannot reproduce/research ammo for particle beam guns right now.