Yes, talk to the recruiter. If nothing else that will give YOU experience interacting with piloting hiring people. At this point in your training you probably can't hurt your future prospects, but you can at least speak the lingo.

Later on, when you're getting closer to competitive for employment, you'll want to ensure that you're well-prepared before engaging with recruiters... treat all such engagements like a job interview.

Also, philosophically long-term, DL and UA are great goals. But don't fixate on them to the exclusion of all other career options...

1. Recent insane hiring aside, for most of my time in the industry your major airline picked you, and if you got called you took the first offer because there was no telling when or if you'd get another call from another major.

2. Desirability of majors from a pilot employment perspective has changed over the years and might change again. SWA and FDX were the hot tickets for many years, with UPS not far behind.