Depends on your definition of profit.
Financial profit: I don't know how much it costs to keep two servers running, so I can't say for certain. However; with ad revenue money and a pass base, I'd imagine there's some money left over to declare a profit outside of operation costs.
As per profit in social profit;
Immense; 4chan is pretty much a cornerstone of a technological age to the point where it gets Presidents elected, creates artists, content, and is a popular hangout for future persons who will go on to influence the media world, and likewise critics of said world.
It's like asking if a Roman Forum is profitable; it might be; but the important thing is the people who continue to visit and be born from this place and not so much the financial end.
Kind of like Wikipedia before it went full pants on head retarded with virtue signaling and leftism.