Help with HSG and IUI questions?

Everything has checked out good with me and my husband. Sperm is good, ovulation is good and no known problems. Both in our late 20's been TTC 16 months. Next step is to have a HSG test done. I dont want to if it is not neccesary. Is it possible to do the IUI and be successful with the HDG. They did do a ultrasound and did not see any bloackage.