I came across this looking for answers about KML extraction from AGS.
However, what you're looking to do is quite easy, presuming I understand it correctly.
What you need to do is use the data extraction tool. The only downfall of this that the user input shape 'clips' the data. However, in model builder you can modify it if you like to us another selection method.
Vector output supports both Shape and GDB
UPDATE: I found a very crude way to modify this so that it essentially functions as a select and not a 'clip' AOI for the input...did this a while back and funny, found this while looking for something totally different! 'Input' is a layer contained in the published map service, 'Stand Selection' is a Feature set, and 'outputfc' is your AOI. Crude as it is...it works. Oh well, back to looking for what I was really after