If you experience your period while pregnant can that affect the results of a HPT if taken while not bleeding?

No. But you wouldn't actually get your period while pregnant. Because your period is the shedding of your lining which would cause you to miscarry. Some woman will have light spotting/bleeding during pregnancy when there period would be due. If you are/ or suspect you are pregnant and are having an actual period you should see your doctor asap.
From everything I've ever read and heard it's very possible to have your period and still be pregnant. And I'm not talking spotting or anything. many people don't know they're pregnant at first because they are still getting their period. I doubt it would effect any results though, but the best way to find out is probably through your doctor.