Newborn two piece vs. onsies

Wasn't sure how to word the title but here is my question. I had a friend who told me that babies can't wear anything except two piece outfits until their cord falls off because it will make it bleed and can make it infected. Is this entirely true? If so how long does it take for the cord to fall off approximately? I'm a FTM so not sure but I've heard around 2 weeks? I'm just worried now that he won't be able to wear any of the cute newborn onesies or sleepers I have for him because he will probably have outgrown them by the time the cord falls off if that is the case. Plus his coming home outfit is a onsie with a jacket and pants so do we need to choose something else?? I could see it irritating it but I thought as long as they were looser he should be OK. Just looking for second opinions. Thanks!