Not like a period does, no. And keep in mind that most pregnant people won't experience decidual bleeding (which is one of the things that leads to the myth that a pregnant person can keep having periods). But, again, if someone is worried they may be pregnant, the way to know for certain is to take a test.
Too, it sounds like you have some anxiety around pregnancy. Have you and your partner talked about that at all, or talked about doing only things that don't pose a pregnancy risk?