Of course crowded and overcrowded can be used to describe inanimate objects:
Ideas which had already been darkly germinating in Ludens's overcrowded mind came vividly into view.
She added the planned cross town route would only be single carriageway and would rapidly become overcrowded with vehicles.
(Examples from Longman)
overcrowded: filled with too many people or things
However, it does not mean that (in terms of collocation) it's natural or idiomatic to talk about an "overcrowded plate", for example. You can do it, and will probably be understood, but it wouldn't be the most natural collocation.
According to the CORPUS OF CONTEMPORARY AMERICAN ENGLISH, these are the top 20 nouns that typically follow the adjective "overcrowded":