I want to know is it possible for a woman whose 4 weeks pregnant to have her period come on and go off the same day and the next morning come back on fully?

I would say no.when you are pregnant you don't have periods.
If you have go to the doc. And explain what's going on.
Good luck

Have you actually confirmed that you are pregnant? Or are you guessing that you are pregnant? If you have actually confirmed that you are pregnant, any bleeding needs to be brought to your doctor's attention immediately- because as stated before, you don't get your period while pregnant.

Bleeding during pregnantcy is never good. Call your doctor NOW!