I'll add that we have been 1 tank / 1 heal (to emphasize that it is not stressful) heroic, and since we started with this, our prot warrior tank has always soaked every annihilate with maybe one external and his own cooldowns. And I never have to throw a single direct heal at him in the transition because of the vengeance he gets (he can easily sustain himself). It might not be as easy on other tanks, and it may not make sense for your raid to do it, but to say it stresses out a healer is pretty much false if it is done right in the correct circumstances.
BUT, remember that normal mode annihilate hits for the same amount as heroic does for the actual cone portion (3.5 million). Of course, the non-cone portion hits only for 360k on normal (as opposed to 700k on heroic) but that part doesn't matter because its the cone portion that matters which is the same in heroic/normal. Thus, if you are truly undergeared or you are going through on normal, it may not be as easy and may not be possible because being at 575 ilvl and doing this is quite a bit different than being at 550 ilvl.
But once you reach that point, it all comes down to how you use your cooldowns and at that point (at least as a warrior) you should not be stressing your healer(s) out.