That would be problematic: It would essentially lock out a huge amount of discovered systems from being colonized, if the first discoverers never come back or don't care about colonizing them. Heck, the vast majority of the systems surrounding the Bubble are already discovered, so they would essentially form an impenetrable "wall" of uncolonizable systems, precluding any expansion.
I doubt they'll go that route. It would be a bit too limiting IMO.
I guess it depends on where the 'new frontier' begins. If they allow us to begin building within 3 or 4K light years of the bubble, there are millions of un-tagged systems in every direction. If we have to start building litterally on the bubble borders, then yes that will stifle expansion if the older players (who were first to tag them) don't come back.
I guess we'll have to wait and see, but I hope first discovery has some role to play in this.