Is it possible for a mouth swab drug test to be able to detect clonidine?

Possible, yes: but highly unlikely. Oral swabs are usually part of a kit that is looking only for drugs of abuse, like opiates, cocaine, amphetamines, cannabis, PCP and others. Clonidine, while it can be abused, particularly together with opiates, is not a common drug of abuse and is not tested for specifically. If they are running full confirmatory testing with GC/MS they will pick up pretty much everything.