You can, but it's not particularly likely and certain doors will be closed. Probably safer to get the degree early on and not have to worry about it.

The degree was not nearly as important 30 years ago, and if we see a big backlash against the cost/value tradeoff of higher education in our society then it's possible the degree won't be that important in aviation ten years from now, especially if hiring continues unabated. But for now it's problematic to not have it.