I think if you took the whole world of poker players and divided them into those who understand the odds (let's say, could quickly tell you whether a flush draw or open ended straight draw is preferable) and those who really do not at all, you'd find the group the understands odds, on average, is a better group of more profitable players.
That said, I think we have to be specific about what we mean by "understands odds". Traditionally we mean a person who can calculate odds and outs and make optimal calls/folds on that basis, and then I believe the above still holds true.
However, I think that short changes some of the people in the other group who couldn't tell you down to the chip the size of the bet they would call with an open ended straight flush draw, yet have played enough poker to understand the basics. Someone who hates math but has played 100,000
hands would probably have a feel for things and based on experience, might understand when to do what. I respect both instinct and the subconscious mind's ability to do things better than my conscious mind sometimes.
So I guess my answer is, if you mean someone who just doesn't care about odds at all, yeah they'll probably suck. If you mean someone who doesn't do the math but tries to use discipline based on experience, I could see that player doing reasonably well too.