I can't forsee it being a problem in EVERY heroic, although you may find one or two that you struggle with, CC is not essential.

When i used to single box we would often clear heroics with no CC using a paladin tank or 2 tanks.

Sure heroic trash mobs will one shot clothies or rogues but Moonkins have armor multipliers equivalent to bears so they should be able to take a hit or two.

Starting a fight with a full stack of HOTs may be a bit risky as pointed out above, but a full set of lifeblooms will be ok, the final 'Bloom' causes aggro on the tank not the healer remember.

Combine Pally AOE tanking capabilites, Salvation & Moonkin armor, and 3 x combat rez if things do go bad, and I dont think a lack of CC is going to be holding you back.