I didn't work as a CNA before or during nursing school, but I think it probably is beneficial. My only misgiving about the OP's plan is doing a CNA program and nursing school simultaneously. That might be manageable during the first semester of an ADN program, but after that, nursing school seems to be pretty much a full-time job.
I did work in a healthcare position during school, in a job that was a mix of some housekeeping tasks and transporting patients to and from tests and procedures. I spent a good deal of my time also assisting nurses and CNA's with baths, dressing changes, and getting pts in and out of bed. It was considered a clinical position, and I was more inclined than some of my peers to spend time with hands on patients, especially after I decided to go to nursing school. Ultimately, though, I agreed with my nurse manager that it didn't seem prudent to tackle learning a new, tougher job while going to school. (At the time, I felt that I was working just as hard as any of the aides, but my job was more physical and a lot less stressful.)
In my program, we learned to do just about everything a CNA does during our first semester, but we didn't do enough to get really good at it. Now, as a nurse, I very much appreciate the work our aides do. If I need an extra set of vitals or to repeat a set of dubious values (our aides usually use an automated BP/HR machine, and I only semi-trust it) I usually get them myself. Aides are often busy getting vitals for the rest of the floor, and when in doubt there's no substitute for hearing with my own ears. I'll help a patient toilet, too, if I'm free and the aide isn't right there. I'm willing to assist with baths, too, but I typically am assisting. It just goes a lot smoother if the aide takes the lead, and I don't think many of them really mind the occassional opportunity to tell the nurse what to do. Plus, I think there's a sort of unspoken assumption that being a guy, I'm expected to be a bit inept with some of the more personal care. It almost sounds ironic, but I think I actually get more respect from some aides because I'm willing to listen. Then, too, some have been around long enough to remember that I always helped them, even before it was really part of my job. But I can see that they do admire those nurses who were aides, and good at it.