Yes you can, but where I live they charge $15 per ticket. You can do the reservations yourself using delta.com. southwest.com.etc and pay no fee,or orbitz.com for a $5 ticket. I use my AAAfor hotel discounts,maps,etc.
I just purchased my airfare through AAA on the website and had no problems. There was no additional charge for the tickets though my local AAA. The fares we paid were about $102 less than what was on the US Air website. I must have gotten really lucky.