Just to clarify, plants can use ammonium (nh+4), not free ammonia (nh3). This is why many terrestrial ferts have a portion of ammoniacal nitrogen in them.
nh+4 and nh3 make up total ammonia nitrogen (tan). The ratio of each that make up the TAN is dependent on pH and temp. As the temp drops/ph drops below neutral, the TAN shifts more and more toward nh+4, and vice versa when the temp/ph rise. Liquid salicylate tests like the API master kit (and others that use the yellow to green color shades) only read TAN, so they don't differentiate between free ammonia and ammonium. This is why people often say that Prime and other ammonia 'binders' give a 'false positive'.
This isn't essential reading, but just thought I'd share for anyone interested.
The summary is that in an alkaline tank, plants will not do nearly as much to combat an ammonia problem as they would in an acidic environment.