Don't think so. I was going to suggest that maybe you could use a dual unit display but callouts are apparently incapable of that.
I consider your request a little odd but I would think dual unit display should be possible but it looks like you can only make it work on the selected entity's dimension. For example, on a counterbore, dual unit only works on the inner or outer diameter (depending on which you select). And forget about depth.
The dual unit setting doesn't apply to the text string modifiers in the dimension prefix or feature callout dialogs. Those are what callouts use.
You'd have to use two dims or callouts to do what you want.
bshand is correct.
This isn't a odd question cause this go's back many many many years. Some of us requested for this typ of behavior for call outs, different units in one callout. Not sure if there's still a ER out there for this. If i have a c'bore that needs to be 3 plcs and the other are fraction, i'll show it in a side view.
@TDB, Thanks for correcting me on the "oddity". Because I've never needed it makes it odd to me I should have said. I suppose there are times where depth could require tighter tolerances than the diameters. Whether you use decimals or specify smaller fractions for the depth tolerance is discretionary I suppose.