Yes, you can do that too but it all depend upon your site location and also How frequent the pressure change will be. If you are in a remote place, you should have the simplest system. Again if the VFD
is not designed for constant changing of head, the speed will rise, fall,fall further rise etc etc. This will shorten the life of your VFD.
I also do not think that there will that much of a price difference. You are not considering the price of the variable speed system. Well, you may save money but the solution is not suited to the problem.