If I submitted a modified excerpt of an unpublished novel to a short story writing competition, and if it were to get selected and published, would it hurt the novel's chances of getting picked up by a publisher? Is it a different story if it wins, rather than merely reaching 2nd-25th 'runner-up' status?
The more ways you can be editorially published while you're looking for an agent, the better. By editorially I mean your work is vetted by an editor. Contests sure. Magazines be they online or print. It can't hurt and it might help. I regularly read Alfred Hitchcock Mystery magazine looking for fresh voices and interesting writers.
Plus there's a lot to be said for periodically changing up what you're writing. Working on a short story as a break from the novel might help you see things in a new light. I'm a great believer in moving furniture for the same reason.
Or as Dad would say to Mum "where do you want the piano this week?"