Probably, but then I don't know what your height limit is. In any case, it will be much longer than your current 15M coils/20 meter operation.
The bandwidth comes almost entirely from the added length. There is another way to accomplish additional bandwidth, and that is by matching the antenna with a shorted stub. The stub and the antenna have opposite reactance changes as the frequency is changed. Properly done, you can about double the effective bandwidth. The drawback is, the you have to have a stub for each band.
The other alternative, is to use a properly matched, remotely tuned antenna like a HiQ or High Sierra. You'll be able to operate the entire band, even on 80 meters. What's more, you'll have better efficiency than your aforementioned antenna.