Yeah, seems likely to me he can still eat (and possibly does, to enjoy the taste), and absorbs the mass from there by some sort of osmosis.
This was investigated more carefully in the 1980's Starman series, where Will Payton, who thought he was an empowered human discovered that the process which gave him his powers (Flight, heat generation, limited shapeshifting) him had actually barely left him human at all. He only breathed because it was a habit, he never needed to eat because his body was a dself regenerating energy source, and his body only formed discreet organs if he felt he should have them (He had fingers because he assumed he would have them, but who the heck thinks about their lower intestine as a matter of course?) and then he's told that he is now sterile, since he no longer has the internal equipment required, and won't be able to create it because it's too complex and he may not have the necessary elements in his body at all anymore.