Yes and no.
The tip adds a bit of thickness to the head vertically, thereby creating slight depth to the mortise. The plug holding that end of the hair in could begin to slip. I can't think of a risk to the bow itself, but you may have the hair come flying out

. Okay, maybe not that dramatic, but still.
Shostkontrabass is right: the tip gives some protection to the wood at the head, and it's a fairly easy fix. Keep in mind that while playing without the tip, you have lost that layer of protection. A simple drop may chip off part of the beak.
Be careful, and get it fixed when you can.