These abilities will be kept! These abilities are more closely linked to their biology and it wouldn't be a part of the frequency to, say, take away Charizard's ability to breath fire just like it couldn't take that from other dragons. Some Psychic powers may not fall into this rule, like telekinesis when it comes to Psychic Pokemon, but that will be a bridge to be crossed if you have an interest in Psychic Pokemon specifically or if someone else would like to bring one in.

As a note (mostly for others, not you), this is a ruling for non-appable Pokemon exclusively -- depending on the circumstances of a character, this may change depending on their own power or magic set.