I am a very accomplished engineer with a BS, MS and PE. I am considering premed school and would finish by the time I was 35 yrs old. Would a school reject an applicant solely on age?

There is no specific age cutoff for medical school. There are many "non-trad" students at similar ages, often as a second career. From your question it's not quite clear -- if you finish pre-med school at 35, you'd finish medical school at 39, and then residency sometime between 42 - 45. You would still have 20+ years to practice.

The real question is whether you're willing to trade in your successful career for a training path that requires long hours, poor pay, and overnight / 24 hour shifts. I used to be able to handle 24 hour shifts with no problem. Now that I'm in my 40's, it's much harder (and my overnight shifts are only 12 hours).

First of all, they can't legally reject you because of age. However, in the real world, this can be a concern. There are many many discussion on the non-trad forum about this topic and you might search some of them out.

Short answer is that even in the real world, 35 year olds can and do get accepted to med school all the time. You have to have all the components on your application that any other applicant has though.