If we don't we still have a A24 3 card?
Unlike Badugi, the way Padooki is usually played is that you do not play a 3 card incomplete hand - you always play a 4 card hand. So if you end up with
then you have what a '7 flush' or if you have
then you have an 'Jack flush' (flush just means a non-padooki lowball hand). Any padooki beats any non-padooki, but if no-one has a padooki then the best 4 card lowball hand ('flush') wins. I assume this is the rule for the game OP is referring to.
This means that it is probably a better idea to discard one of the deuces and draw two cards. The reason for this is that if you do not make a padooki with one of your two cards then you have a better chance of making a decent flush (as opposed to pairing up or making, say, a K flush). I would have to run some maths on this though to be sure.
That said, if you only draw one card then it looks like you have already made a padooki and are simply trying to improve on the final change. So it gives you a decent chance of bluffing the river if you miss (but less implied odds if you hit).