Yes, I store all my dishes, glasses and platters in my frameless upper cabinets. It's been several years now, and I have never had a problem.
Frankly, you should be more concerned with the quality of your cabinet brand/manufacturer/maker for the stability of your cabinets than concerned whether they're frameless or not.
And of course, undercabinet lighting is installed with frameless cabinetry. Make sure your cabinet order contains a "light rail" which is simply some trim at the front edge of the underside of the cabinets to shield the undercab lighting from view. A Light rail is very standard, though you can get them made with a simple design as Newyorking described, or a little more ornate.
Other tips regarding undercab lighting: if you are planning undercab lighting, the distance between your countertop and your upper cabinets should be 20". That allows 2" for undercab lighting, and the standard 18" distance from countertop to upper cabinets. Furthermore, install your undercab lights toward the front of the upper cabinets, NOT toward the rear. Your goal is to light as much of the counters as possible. If you install the lights toward the rear, you are wasting much of the light beam on the backsplash. For some reason, some electricians insist on installing undercab lighting toward the back--I think it makes it easier to install. If your electrician is one of those, stand your ground and have him install them toward the front.
Here are a couple of other threads for you to read:
Thread called Cabinets Frameless vs. Framed
Thread about Frameless Uppers
Q