It makes sense, but more so in a case where you are doing something that will make the knife steel fail at your chosen angle. If we are talking mostly about wear, there is more to look at, I think.
I tend to think that a convex edge, done right, is a stronger edge, but as Ken mentions, it really dulls faster. It is what I prefer for heavy duty cutting tools… Kuhkris, machetes, etc. It makes sense if you think about the geometry, a convex edge is thicker right behind the edge, as the edge wears or folds it gets thicker faster too… hence more dull more quickly.
If anything, unless you are OK with a dull edge, you need to do more maintenance. When you do this, it is also more work to get it back than the V.
A more acute “V” will tend to be thinner right behind the edge. Unless you apply force that exceeds the steel’s ability to take it, as the edge wears, it will be sharper longer.
Now this is all theory, I don’t have micrographs to prove it, but it fits well with my experience. I convex the edges of all of the knives that I will use for chopping or heavy duty cutting of any kind. They definitely lose the original slicing ability quickly, but they take lots of abuse and edge integrity is maintined… and they stay good enough for chopping tasks. I wouldn’t use them for making feather sticks… after a few cuts on something else.
I have done some kitchen knives on the belt grinder (lots of them for cutomers, they love them…not as picky as me) ..off platen, slack belt. This gives a nice convex edge which will push cut tomatos, but it doesn’t stay that way long at all. The same knife at 17 degrees on the WEPS with a fine microbevel at 20 to 22 degrees (half dozen or so strokes with the 1200 ceramics) stays sharp considerably longer. It may not survive an encounter by a ham handed knife weilder with a hard bone as well as the convex edge… but I really try to avoid that 
The V is also easier to touch up than the convex edge. Usually a few strokes on a bench strop with 3 micron paste for me brings it back nicely. The convex edge needs a second visit to the bench grinder…
To wrap it back to what you said Tom, I tend to think the results with a more obtuse angle will also lead to a more significant loss of sharpness more quickly than a more acute angle…if y we do not exceed the steels abilities… of course.
Phil