This is all fully possible, but I think the R&D involved in getting it right would likely cost more than erecting a 100 foot tower (depending on permit fees if there are any). If you run lipo batteries - a charging station won't work because charging rates are far lower than discharging rates and if you don't follow the recommendations, the battery will eventually explode (probably sooner than later). You'd almost need a battery swapping station and you'd have to have a lot of batteries so they could cool. Plus, landing and taking off every 20 minutes or less is going to kill your ability to have good coverage.
Even if you got the power worked out to avoid using batteries (lighter wires, solar, etc.), I think you're going to have a lot of component failures if you run the copter straight for even a few days at a time. Weather will always be a big concern. You're going to have to have a waterproof copter, and the good waterproof frames on the market are up near $1,000 or more. Also, constantly keeping stable at 100 feet, especially in windy conditions, will eventually stress your props and they will snap off if they don't vibrate loose and fall off first. There are a million other things that can go wrong as well.
A 100 foot antenna tower kit with guy lines is under $5k (depending on the wind speeds you expect).
http://www.solidsignal.com/100-foot-antenna-tower-th.asp
Or, you could create some kind of FPV blimp tethered to a 100 foot long fill tube and you could pump helium into it every week or so from the ground.