A home pregnancy test will be positive with an IUD if you are pregnant, but it should not give you a false positive. I have had a previous pregnancy with a Paragard IUD- if you've had a positive pregnancy test you should schedule an appointment with your OB. They may want to do an early ultrasound to determine the placement of the IUD and the placement of the baby. You can still have a healthy pregnancy even with the IUD in place.
So I totally misread that--my brain is spacy today. An IUD will have no affect on an pregnancy test, as it looks for the hormones created by pregnancy. Nothing but hormonal things (such as a trigger shot which contains the hCG hormones) will have an affect on those.
You need to see a doctor ASAP for blood work, as well as an ultrasound to see where the IUD is.