No not really. "AIs" today are entirely digital LLMs that can be copied, shared and redistributed for a marginal fee already. "Collecting" AI would make absolutely no sense, especially since most of the AIs worth collecting cannot be used for commercial/museum-fee purposes. The only such thing that will exist in the future are the people that digitally archive today's model files.
Music can be copied, shared and redistributed for a marginal fee. Text even more. Nevertheless, you have record and book collectors. What's the difference?
I collect them using ollama. My favorite go to is nous-hermes2-mixtral, though others have things to say. They're all distinctive (phi3, llama3, wizardly, etc.) and can be a riot with the right prompts.