Yes. In that case they will probably ask you about your info, check in their system, you would get a fine for not carrying your documents, and that’s it.
A BIG difference, however, is that they will not even approach you if you are not doing something you should not be doing. In other words, they will not bother you while you’re sitting on a bench or taking a stroll.

Yep

Why do you assume I don’t have it?

As I said, I’m not from America, I wouldn’t know your laws, that’s why I’m asking

Would someone care to explain why would they not show their ID? Is it better to get detained than showing your ID, unless you have something to hide?
Anyway, in my country we are required by law to show police officers our IDs when asked.