If you somehow managed to get the air out, and have a good, firm brake pedal now, there won't be any problem until you work on the system and need to bleed it again. If the brake pedal is soft or spongy, you must get the bleed screw out. Otherwise, I would leave well enough alone for now.
The broken off Easy Out is a classic problem. The original problem wasn't that you couldn't get a grip on the bled screw, but that it was frozen. It is much easier to deal with that problem before you twist off the bleed screw and create another one. If it doesn't seem to be coming with a box wrench or 1/4'' drive socket, don't just pull harder. Often pounding on it with a small ball peen hammer, will flex things enough to allow it to be turned out. If not, the next step is to heat it with a torch and cool it quickly. Be careful what else you heat and take it easy, very easy on aluminum parts. Those cases where an Easy Out works, usually are do to the heat and vibration of drilling the hole. If you apply the heat and vibration before needing the Easy Out, you can skip that whole step. Penetrating oil alone, seldom solves the problem. It also avoids buying a new bleed screw. Usually they are not expensive, but nobody may be open that has the right one in stock. Some of this hammering and heating is best done on the bench. Rubber parts not removed before heating much will be ruined. Bottom line, don't bust the **** thing off in the first place.
I strongly suggest removing bleed screws, cleaning them up, and coating with a silicone grease such as Sylglide. Anti seize may be OK, but I am paranoid about applying any hydrocarbon to any brake part.