HTupolev

The effects of rim width on tire height can be a bit complicated, but no: within the reasonable scope of rim widths, the impact of rim width on height is less dramatic than you might expect, and a wider rim will often result in the tire inflating both wider and taller.

A (simplistic) way to visualize what's going on is to imagine that you've got a tire that always inflates to a perfectly round profile. Suppose you've got a rim with an internal width of zero, squeezing the tire's beads together. This causes the tire to form a complete circle:



Now imagine a second rim, where the internal width is equal to twice the diameter that the tire has on the zero-width rim. Now we have this:



The tire is now half of a circle with twice the diameter than before; the circumference has doubled, but the tire only exists across half of the new circle's circumference. The radius is the same as the old circle's diameter, so the inflated height is equal.

In practice, the height doesn't stay the same across the range of rim widths, but it also doesn't just trade height for width.

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But I also don't understand your objective. Insofar as tires serve as a suspension system, the main value to using a bigger tire is that it achieves more suspension travel by inflating taller. In order to avoid bad behaviors like bottom-outs, it seems like a wide-and-short tire would need to be pumped just as stiff as a narrow-and-short tire.