Most domes have these little air-holes on the top and/or sides that you can slide open. You'd do this after 5 days to a week, so long as once you do the plants aren't beginning to wilt. If you have good visible root growth already then the dome can probably be removed entirely, or you could just transplant them into whatever medium you plan on using and start the veg period in earnest.
I'd say yes, roots will probably begin to grow a bit quicker once air exchange is occurring, as roots breath oxygen. The reason for the dome in the beginning is to keep the humidity high, since the cuttings don't yet have any root system to support themselves and will wilt otherwise. It also keeps everything sterile and helps prevent any pathogenic microbes from attacking the cutting, as fresh cuttings are extremely vulnerable to infections. Once they have good root-mass, however, they can pretty much fend for themselves.