It is possible, to some degree. When someone gets info on you to see your away message, they query your computer for the away message (it's not like you store the away message on AOL's server).
However, if you're sniffing the network traffic and notice your away message going out, you'll be hard pressed to figure out who owns that IP address.
The better answer: you can tell if/when someone gets your away message, but not necessarily who.
Disclaimer: the above research was done using Trillian, not AOL's AIM client.
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