The amount of energy used will increase proportionally with the number of planets, provided that we are just talking about one-way one-time colonization per planet. Energy use vs. population is per planet and by technology, not over the whole inhabited area, since they would need to be independent.
If we are talking about an empire with trade and cross-planet sales trips and military actions, then I agree with you. The energy wall will hit pretty hard and the empire will fall. But the colonies will still carry on, either colonizing slowly, creating more empires doomed to fail, or whathaveyou.
With a 3

expanding sphere (or even a misshapen blob), it is likely that there will be gaps in places limiting expansion, but very unlikely that the whole area will be an isolated island. Possible, but unlikely.