I thought the 2006's came with a K24 that was a 2.4 not a 2.2.
look for a K series transmission, it doesn't necessarily have to be from an accord, but it makes things easier and keeps the stock ratio's meant for the car, along with less potential for issues. I'm not very familiar with their chassis, nor dealing with automatics.
Older accords used the H/F series engines and the V6's were J series or something like that.
and the answer is NO your car is k series. the engines spin in opposite directions for one.