In this question asking about a homebrew mechanic involving exhaustion, the accepted answer points out an exploit using a moon druid's combat wildshape - Taking the form of an elemental would avoid the downsides of the mechanic as elementals are immune to exhaustion. The answer then goes on to suggest that the druid would need to have greater restoration cast on her to remove enough levels of exhaution before the wildshape was dropped that the druid does not die outright.
Unless I've missed it, there isn't a specific definition for "immunity" within the rules, so we must read that word with its regular meaning in English. In particular, creatures are listed as being immune to the condition itself, not to the effects of the condition (or "asymptomatic" or a "carrier" of the condition or similar language).
The case in the linked question is even more complicated because exhaustion has multiple levels:
If an already exhausted creature suffers another effect that causes exhaustion, its current level of exhaustion increases by the amount specified in the effect’s description.
As such, my reading is that since the element is immune to the exhausted condition, this clause would never trigger - the elemental cannot be an 'exhausted creature'.
Is this interpretation correct, or is the condition applied but ignored? (And particularly, could elementals gain multiple levels of exhaustion whilst being immune to the condition, for the purposes of ending wildshape for example?)