If Mewtwo "Energy Absorbs" a Rainbow Energy and then Venusaur "Energy Trans" it, does the receiving Pokémon take damage?
Nope, it only does [places] the damage [counter] when you play the card from your hand.
Source: WotC Chat (2000-06-22)

Relevant cards

Note: All applicable cards may not be listed below.
HGSS1_104
PL1_121