Google+ – How to Remove Cover Photo

No. Each Google+ account is tied to a Google Profile account, which can have only one primary email.

If you're only trying to remove you Google+ information, then I would suggest selecting the option Delete Google+ Content - I don't know if deleting your entire Google account will affect login to Gmail, but you can read more about deleting your account on the help article page

This is another article that highlights only selecting Google+ content to delete. Don't select the entire account, if anything start with just Google+ content as the first trial step.