What you seem to be discussing is not normally known as a loop invariant.
"Loop invariants" are normally understood to be a form of invariant, i.e. something that doesn't change, not something which does change from iteration to iteration. A loop invariant is an assertion about the state of your program which is true at the beginning and end of each loop.
For example, we might make a trivial loop invariant like this:
vowels = "aeiou" for c in vowels: # pointless loop invariant assert c in vowels
Invariants are normally assertions, which may be disabled without changing the meaning of the code.
I'm sorry, I don't see any benefit to your proposal aside from saving one line and one indent. I don't consider that sufficient benefit to make it worth adding redundant syntax to the language.