I expect so - the backtrack will record any signal it receives at the 1/4" input jack.I presume you're using some effects on the amp (other than simply volume) to affect tone? If not, you might be able to go directly from your akai to the BackTrack.

If using the amp you may have to fiddle with levels because the amp out is likely line level and the backtrack input is likely instrument level. If your amp has an instrument level output it might work better. Also you will need an adapter from your amp out to feed the BackTrack 1/4" input.