Yes. When a frame (or object) rusts it can get weaker. As metal oxidizes (rusts) you lose the solid bond. When you clean up the rust (usually heavy stuff, not just a light surface rust) you are taking off material that was part of a solid structure. If its really bad, you will notice spots that are thinner than others or even spots that go all the way through.

My buddy had some wheels on his truck that were so rusted that he could take a screwdriver and poke right through the wheel with it. Needless to say, they were replaced immediately.

Hope this helps. I tried to find the right words to explain it clearly.