I think Sam would be how shall we put it power drinking every single demon on the planet.
Two possibilities:
2) There will be a throw-away line about how Sam tried it and that it didn't work (either because of the lack of a soul or that his body came out the cage without that sort of ability).
Logic doesn't really support this. Sam has died at least 3 times previous, and his being returned to the mortal plane had no impact on his abilities.
Sam soul has already been separated from his body and his body still held the "Seed" of being able to harness demonic energy.
If Crowley had the ability or any other demon that held or could make contracts that would remove Sam's ability to either house or harness those demonic abilities then another powerful Demon who could also make and hold deals who had great power would have done so earlier. And we know such a demon did live and absolutely was motivated to end the threat that was Sam, and that was Lilith. And while she couldn't blast him away, she absolutely could deal.
Option 2 is really just throw-away logic for if the writers want to take the easy route (basically the "it doesn't work anymore" with blah blah blah attached). Option 1 is the more interesting one. In fact, I'm not even sure that it would occur to Zombie Sam (which is a great moniker, by the way) to even try demon blood. It was mostly the emotional side that took him down that route. His intellectual side always stayed away from the blood unless there was a really good reason to try some.