Can I legally reverse engineer AI generated software?

If you have the source, why would you need to?

Can you even put terms and conditions on this supposed public domain copyright free compiled software product?

You can put terms on anything, but you can't protect the underlying asset if someone breaks your terms. Think of the code produced by Grsecruity that they put behind a paywall -- people were free to release the code (since it was licensed as open source as a derivative work), but obviously Grsecruity was able to discontinue their agreement with their clients who would do so.

Is the compiled version even different than the raw AI generated source code in its ability to be licensed?

People aren't generally licensing compiled binaries as open source, since you can't produce derivative works from them. But I think that if there is no copyright protection for the work, compiling it doesn't change the copyrightability. Curious what you think.

What rights does one have to AI generated code? Be it compiled or source. It’s surely not just communal.

Why is that surely the case? It is public domain - that is the most "communal" you can get for copyright.