Andrew: Naturally it is possible and it can be done with great success, but this depends on many factors, some of which the architect may have no control over.
Some architects have more ability convincing their clients about the value of recontouring portions of the green surfaces, if in fact it is needed to begin with and others simply will be powerless. I think it is important to first determine if recontouring is even necessary. Not always, depending on how old the course is, should the design integrity be preserved? will this be needed. I think you also understand that a project like this often isn't as straight-forward as you might think. There are many decisions being made and countless other factors being considered behind the scenes that influence the final project scope. I would agree that if the greens REALLY need recontouring, the architect should do everything in their power to explain/show the project committee the value in this work as well.
If the architect is not able to convince the club, well then the ethical/business side of the practice will make the decision for architect on an individual basis. That is a whole other discussion.
Costs will also influence the decision and while the architect may be right to recontour, the club will make the final decision in this regard. Perhaps it might be better to scale down the project and rebuild fewer bunkers and do the recontouring on those green sites instead of just doing all the bunkers. This may build momentum in the membership and allow the project to continue with better financial support for phase 2 the following year. Maybe even the architect should attempt to convince the club not to do any work at the moment and wait a year to raise more money to support the recontouring as well? They could always choose one green site with bunkers and do this one as a trial and show the club the benefits. This might generate more support for your concerns.
When you say the bunkers look unnatural, how so? Was the style changed to no longer fit the original design? Do they not relate to the green surfaces?
Certainly the bunkers could be redesigned and rebuilt to work well without touching the green surfaces, but this may not be the best approach, or it just might be what the doctor ordered?! Also, it could be that the architect doesn't know how to approach recontouring the greens?