Not necessarily. While VO2max can and will rise, MHR tends to be a reasonably fixed entity. It could change by a couple beats, but generally not a significant amount. As such, your sport specific MHR should correlate to 100% VO2max regardless of what that level is.Would a high VO2max mean that you can train at HR levels higher than the bands recommended by most HR training programs?
With regards to the HR training bands, it is not the specific changes in VO2max that will cause a change in training bands. Instead it is the changes in aerobic and anaerobic thresholds (if you put value in such concepts) that will cause the changes. As your fitness increases, these levels can rise to higher percentages of VO2max; leading to higher HR bands to achieve the same stimulus as prior years. This is where outside testing is required to accurately determine HR training bands for the individual.
That being said, unless you are elite or planning on becoming elite, being close to the "optimal" training bands will do you fine. Use the general bands and modify a little based on feel. If you are supposed to be working hard, but it continuously feels easy, odds are you can push the band up a little. If it's supposed to be easy but it feels hard, drop the band a little.