What is the keyboard in question? My low-end Yamaha models have settings in their Function menus to control whether or not the MIDI data for the auto-accompaniment is to be transmitted.
But the Alesis LineLink is for transmitting and recording the keyboard's audio output, so the auto-accompaniment's audio should be getting mixed in with the other audio output anyway. If you're wanting the auto-accompaniment's MIDI output, the Alesis LineLink has no bearing on that.
As far as the keyboard's MIDI output, multitimbral 16-channel keyboards generally have many different "parts" that they can output, where "part" can be a "keyboard part" or a sound you play with the keys (e.g., the "main voice" and "dual voice" and "split voice" on my Yamaha models are 3 separate keyboard parts), or multiple parts used for the auto-accompaniment (Yamaha uses 8 auto-accompaniment parts, but I don't know if it's "industry standard" to have 8 parts for the auto-accompaniment), or 16 parts for the 16 channels of a MIDI song file, etc.
Thus, a part could be thought of as being like a MIDI channel, although it's not the same thing; it's more like how the OS of the keyboard is programmed to divvy up and utilize the available tone generators.
Anyway, a keyboard that has an auto-accompaniment feature will generally have settings somewhere in its menus for selecting which specific parts or types of parts you want to output via MIDI. Depending on the keyboard model, you might even be able to choose which MIDI channel you want to use for a particular part. I don't have that on my keyboards; I can choose whether to send the keyboard parts, style parts, and/or song parts, but not whether to send a specific part on a specific channel. So you might need to review your keyboard's settings to see what options are available to you.
EDIT: Sorry, it sounds like you might already know about "parts," but maybe that info will be of some help to others who read this thread.