No. Corals need to be acclimated, but not QT'd.
There are (4) main ways that people add corals.
1.) remove coral from bag and place immediately in tank
2.) temperature acclimate in bag for 10-20 minutes, then add coral to tank
3.) temperature acclimate in bag for 10-20 minutes, place in a coral dip solution, then place coral in tank
4.) temperature acclimate in bag for 10-20 minutes and / or drip acclimate for 2 hours (recommended for SPS), use coral dip, or not, and then place in tank.
The coral in all cases will also need to have a light acclimation period in which the coral is placed in the lowest light, and then subsequently moved to the highest light that makes it happy, ie no bleaching or browning.