Does it increase your chance to get into dental school? Absolutely. Assuming having 2 candidates exactly same numbers, but one with DA experience and the other with none, it's a pretty easy choice.
With that said, some of my DAs are in undergrad and they have been doing this since their high school, and they have 2-3 years of experience already. They are now FTDA. They are truly the best DAs I have in the office. They don't show attitudes, great work ethics, follow docs really well, and are always curious about everything dentistry. It's an absolute joy to work with them, especially as a former teacher, I love to teach. The other day I taught them about cervical burnouts because they thought they were cavities. Fun!
With that said, one is kinda switching her direction into hygiene because she doesn't like some of the things that a GP does (surgical ext...endo...) and not really interested in specialties. Without this experience, she might have jumped into dentistry and regretted her choice far too late. Another girl got more interested in dentistry while working as a DA.
Why an earth are you thinking 10+ years if you're in undergrad now? If I could change anything, I wish I would have gotten into dentistry a lot sooner. I spent some of my earlier life doing some things that I wanted to do, including teaching in college where I spent the most years, but those years would have given me a lot more opportunities in dentistry had I started earlier.