It's not even profitable _now_ with all their monetization. But their overhead is millions of $/year. There is precedent for non-profit sites of that size but it won't be easy.
Honestly with the amount of charity fundraising that reddit does, I bet they could pull it off. Just recently someone accidentally gave $15k to charity and in response, a bunch of users raised an additional $55k [1]. If they did intentional, annual fundraising with clear goals I wouldn't be surprised if reddit the non-profit organization could be self-sustaining.
But I'm just some guy on the internet who doesn't actually know anything about non-profits.
I also suspect their tech stack is a huge ball of bloated inefficiencies that costs them much much much more than the bare metal and the bandwidth would.