I've been looking at a headset in the FS section that has a 27.0mm crown race. The fork I would put it on is sized for a 26.4mm crown race. I would be using 25 5/32" loose ball bearings in each cup. For the sake of argument, let's assume the bearing cups of the headset fit the frame fine.

Could I theoretically use any 26.4mm crown race with the loose ball setup? If not, why?

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...you can probably find a crown race that will work, but that will not be "any" of them. The reason involves a number of factors that make it generally a poor practice to mix headset parts. I don't really want to try to elucidate all of them, but I've certainly done it myself on occasion with satisfactory results.

If you picture a crown race and the bearing cup that accompanies it, then redraw the curve on one, or look at a couple of headsets and mix and match the parts to see how the cup overlap can differ with one race or another, you'll begin to see some of the issues. Can be done, but it's usually easier to just buy the entire correctly sized headset you need, and it often works better.

Not all headsets use 5/32" balls. Your donor race would have to be from the subset that does use 5/32" balls. And not all crown races are the same thickness. If your donor race is too thick, it may change the overall stack height enough to prevent secure engagement of the upper locknut. If it is too thin, the edge of the lower pressed cup may drag on the fork crown.

Mix 'n' match is very much a trial and error affair.