Would silica gel inside my bike frame be effective in preventing corrosion? I ride my bike in all weathers, and I'm concerned over the possibility of rust forming inside the frame and going undetected.

I can't easily obtain FrameSaver or the like, so I'm thinking of dropping a packet or two of silica gel desiccant inside the seat tube of my steel-framed bike. I'm concerned that its effect won't last as long, or that it will be rendered ineffective should a small amount of water pool inside my frame after riding in the rain, soaking the gel packet.

Does anybody have any experience with using silica gel packets to prevent corrosion? Does it do a comparable job to corrosion-preventing sprays?
No, it wouldn't work as long as the frame is not hermetically sealed to keep water from entering (I don't know why manufacturers don't do that).

The silica gel can only absorb a tiny quantity of water, a drop or so per packet, then it becomes ineffective. It is only effective to absorb water vapor.

You can bake it in the oven to regenerate it. 
If you want to play with it, there is a version with a water-sensitive dye (blue -> pink, now illegal because of cobalt content) and orange to a bit less orange. If left open, it will change color quickly.