Is there a chance? Sure. But I'm not sure how much. The only people who really know how the apps are scored are in HR, and they won't be posting here.
Your best bet is to go the CTP route with a regional and get both boxes checked. Most don't require the CTP to be paid back, just any bonus money you take. So park the bonus money and pay it back if hired by a legacy/LCC.
Will you fly weekends with a regional? Yup. But you know what? Umm... the legacy airlines fly on weekends as well. Much of the flying at a regional is the same, just a smaller airframe.