I have not tried the following myself so won't say that it will work.
Standard configuration of the AA is that one of the prompts contains "Press 2 to make a new call". Don't see why you cannot enter a speed dial there to call a number configured in your speed dial list.
Note that the AA has its own Digit Map and OutBoundCallRoute which you may need to configure. You could set the digit map so that it contains only the speed dials you want forwarded to. That prevents callers from making calls to other speed dials or 'normal' numbers.
Also if calls are coming in on a GV number I doubt you can have another simultaneous call going out on it, so you would need to use another GV or SIP SP. (And unless the provider permits spoofing it will be impossible for the mobile to receive the CallerID of the original caller.)
Update with further thoughts.
You don't even need the 3 key presses of speed dial. A single digit or more can be converted to a full phone number with the <number1:number2> construct in the digit map eg <2:777 234 5678> or <23: 403 654 3333>.
If this intended for callers who won't know the codes to enter you can record your own prompt to inform them and use that instead of the default one. For example "Press 2 then after the prompt enter 20# for Bob or 23# for Alice."
How to record your own prompts and some ideas similar to your request are in
http://www.obitalk.com/forum/index.php?topic=12567.msg80841#msg80841. The AA section of the Admin Guide is
http://www.obihai.com/OBiDeviceAdminGuide#_Toc367543095
