Is there a limit to the amount of addons/mods I can have installed in Garry's Mod?
Yes there is somewhat, not a limit of what content or anything however there is a limit on how many Lua files may be loaded at once.
The current limit seems to be 4096. I doubled it so it should now be 8192. If that didn't change anything let me know, maybe there's another hardcoded limit within the engine and it might be a bit more tricky to remove.
So you can have as many addons so long as the number of Lua files does not exceed 8192.