I don't think it'll be an insurmountable task, but the gear you receive with a boosted character sets you up to start running Heroics right away. More often than not, at least in the random groups you get with the LFG tool, tanks are programmed these days to pretty much just rush from boss to boss, gathering up as much trash as they possibly can kill it en masse and get it out of the way - so you'll have your work cut out for you right off the bat, especially if you don't have much experience as a healer.
And just as a heads up, tanks who use the LFG tool for random heroics are usually some of the most laughably impatient players around. So if you lag behind at all on your healing, be prepared to deal with a lot of whining.