If I put Models inside of ServerStorage, will it drop frame rates for users or is it literally a storage that doesn't influence the game's performance if not called by a script?
Normally if you'd store an object in some place like lighting it would cause a lot of network traffic between players in the server. But putting them into the ServerStorage makes the objects server-side so there wont be any network traffic used up to load the parts and etc. However local scripts cannot access it since it is ran server-side. I normally use ReplicatedStorage in that instance.
In shortest terms, no, Serverstorage and replicated storage are great places to store things without losing FPS,