Asthma is supposed to trigger once every ~6 hours whether you sleep or not, unless you use stimms or depressants (stimms increase the chance, depressants decrease).
While sleep interruption is probably highly annoying, this trait is otherwise nearly harmless. While awake, it will simply consume a charge from an inhaler - item otherwise nearly useless that commonly spawns and starts with 100 charges.
Now that I think about it, this trait looks like everything I dislike in traits. Nearly harmless but annoying.