It is probably not defined because the resulting region is a surface rather than a filled body.

Is there a simple call to convert a surface to the enclosed solid?

This relates to that discussion, and right after that I asked myself exactly the very same. I did not find a solution. As Sander pointed out, the region in question is not solid - and there are various ways to check that, e.g.:

reg = DiscretizeGraphics[hullForm];
Through[{RegionEmbeddingDimension, RegionDimension, SolidRegionQ}[reg]]
(**  Out:     {3,2,False}  *)

One way to define this as a solid region is doing it implicitly:

regimpl = 
  DiscretizeRegion@ImplicitRegion[0 < x < 108 && y^2 + z^2 <= curve[x]^2, {x, y, z}];

Now you have:

Through[{RegionEmbeddingDimension, RegionDimension, SolidRegionQ}[regimpl]]
Volume[regimpl]
(*  Out:   {3,3,True}  *)
(*  Out:   13042.690  *)

Yes, I've done the integral separately. Not a very informative error message. Thanks!