Ableton Live pretty much processes everything as stereo. For example:
If you create an audio track and record from only 1 mono input, Live will record the information and store it as a mono audio file; but any effects or plugins that are added will behave as if it is a stereo track, Keep in mind though, even though it is coming through on 2 tracks; as long as both sides are identical, it is a mono signal anyway.
Also, if you drop a mono sample into a drum rack or sampler instrument, it will still come out as mono, but any other effects will treat it as if it were stereo. If you would like to ensure things remain mono, you can use the Utility effect to either set the stereo field to 0% or set it to get signal from only the left or right channel.
I hope this helps.