No. Black's pawns are just too far advanced.
Can White draw this?
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Actually, white could potentially win if he were first to move:
1. Re6 Kg7
2. Rxe5 Kf6
3. Rf5+ Kg6
From there, white could start stripping pawns from black without leave.
In fact, it doens't matter who moves first. White will win.
No, it's lost for white, black has the plan to move the king to g7 or g6, rook moving to h8 to h2 to xg2, there's no stopping the black g-pawn from queening because the white rook and white king are both too far away. White can munch pawns e5 and a5, but it's resignable.
But you might want to check with an engine, they generally find some fantastic resources in lost positions.
You can use chess engines