The RNG gods play 40% if the role in my opinion. But the way I see it is how. Let us say if it was a mirror match, it is a 50 50 matchup. However, when it is a very expensive good deck against a f2p one, the odds are 30 70 for the expensive one. This means that you still can win but the odds are more against you. In addition, we have to keep in mind cards drawn, starting hand and all that makes huge difference. So yes you can win I agree but we can't deny that expensive cards gives a slight edge.
RE: Is it possible to compete at Mythic rank as F2P? Can you win vs $500, $1600 decks? Yes, you can!