According to this guy's guide, about half way down in Gear Stats, attack speed is indeed a critical stat, as it does increase your healing animations' speed according to this line:
This bonus is quite noticeable and important for priests. It increases
all our healing animations, including circles and even target heals.
This is a must and you should aim to have two of these rolled on your
enigmatic staff. At the example above, the staff has "double" attack
speed stats rolled.
This guide also states that attack speed is a useful stat when it goes over all of the stats.
Which of these affect a Healer's raw healing power?
None of them! Pretty cool, huh? Our heals cannot crit and Power/Attack
only affect damage dealers. The only combat stat or stat modifier
that's of benefit to a healer is Attack Speed. That allows us to get
off our healing and buff abilities faster, so it's something to look
Finally, someone on these forums says that you heal faster with it. That topic is from 2012, and it says that there can be disadvantages to attack speed. This mostly seems to be the ranges of melee attacks. These range changes could have changed since this post.
Overall, I've seen several places say that it increases your healing speed, so at the very least, it shouldn't hurt it.