Not necessarily. If you list say 15 years of experience and a degree with no date, the reader will assume you are "at least 37". We're just trying to get an interview here - when you show up they'll have a better understanding of your actual age (in most cases), but at that point they're committed to the interview and hopefully the candidate performs well enough where age won't be a factor in any decisions.

At this point in my career, if I was prepping a resume, my education section would have one line:

Wossamotta U, Computer Engineering, BS

Doesn't need a date or any details, my job experience is more relevant, and if they've got questions, they can ask. If I had another good stint of work, I could just put Education: yes. Also going to leave off my college jobs and write Recent Experience. Although I got my last job through networking without writing a resume, and I'd expect the same for future work.

I list education without graduation date because I attended for 2 semesters. I've never considered it labeling me as old, but I've never had a hard time getting jobs, with the exception of a few jobs near me that only hire out of specific universities.