You need to encounter them twice in order to be allowed access to Poni Coast, Poni Gauntlet, and Battle Tree, otherwise Looker will block you off from that path until you've had 2 encounters. Whether those encounters end in catches, KOing them, or even simply running away is irrelevant.
Once those encounters are over with, if at least one of them didn't end in a catch, the beast will remain available in Poni Grove's encounter table until you have specifically caught two copies. You can go do whatever other things you want in the mean time, it'll still be there.
