Yes. There are many formats where competitive performance and cost of play are largely uncorrelated. However, because the most popular format of Magic has rotating card pools, this may be true some years and untrue in others. Recently there has also been a significant increase in popularity of an all-commons format known as Pauper.

For Limited gameplay, where you build a deck out of packs opened at the table, the cost of entry is essentially the cards. So paper MTG is pay-to-play, not pay-to-win.