What about the inverse? My 1/8" wheel just exploded at work and I was halfway through a pile of 3/8"LP chain. Can I use the 3/16" wheel to get a "good enough" cutter profile?
You can always try and get back to us with the results! Again, you will end up with different profiles - 'good enough' might depend upon what you are cutting. Remember that you also have to be able to clear the depth gauges and tie straps with the larger wheel. You may have to change your grinder head tilt angle to fit the wheel in there. Might be easier with worn chain that has more space from previous sharpenings.
Another solution for the 1/8" wheel would be to dress the radius needed for the chain on the wheel like it is 1/4" wide. Only one side of the wheel does any work.
I don't entirely agree that only half the wheel does any work - the wheel profile determines the profile of the side plate cutting edge, which does the heavy work of cutting the wood fibers when cross cutting. But in the situation the OP describes, it might work. That is an interesting idea.
Philbert