Playing chords which are already played on the track will not add to the music you produce very much. In current scenarios, many very good keyboard players play to a track in live performances, however, their additions to the music are worthwhile and interesting embellishments more than chord beds. Some of us did special mixes of tracks which did not contain piano or organ, and played the keyboard part "live".
You are correct that it doesn't make one a keyboard player to play to a track. However, a keyboard player made by study and practice can add considerable value and entertainment to a track.
In my mind, "can't play with two hands" is not a valid reason to play chords which are already being played. It would add a "jam" feel to the music which is, at best, superfluous, and, at worst, detrimental to the composition.
My advice is to not worry about playing chords so much, except when you play without a track. Concentrate on adding "fills" and "leads" which are complimentary to the track. One real nice feature is to play harmony to fills already on the track, or in round or fugue with track figures occasionally.
Concern yourself primarily with your musical content which includes your track, and don't worry about "two hands" or "one hand" Iand remember, that some of the most valuable ornaments in music are rests)....
take time, and consider carefully what you will play to your tracks. Practice it well, so that the sync and the "groove" of the track mesh with your playing. Adopting the "groove" of other players is good subject for practice.