No.
Level X pokemon are considered just POKEMON while in your Hand, Deck and Discard Pile. Hince why Celio's Network and Bebe's Search can get a Lv.X because on the card it says search your deck for a POKEMON, show it to your opponent and put it into your hand but a card like Roseanne's Research can't get a Lv.X because it says BASIC POKEMON or Professor Elm's Training Method can't get a Lv.X cuz it says EVOLUTION POKEMON.
Yet once you level up a pokemon then it become the same stage as the pokemon it leveled up. Example - Darkrai ---> Darkrai Lv.X..Darkrai X would become a Basic, Gardevoir ---> Gardevoir Lv.X...Gardevoir X would become a Stage 2.
Hope that is clear and helpful :thumb: