Depends on what you expect. Racers run different compounds front to rear all the time, even left to right depending on the track. But, they also do a lot of tuning to make that work.
The biggest thing to realize is that your tires will have different handling and wear characteristics. That may actually be a good thing if it's matched to the cars set up, as we already know that the front and rear tires wear differently anyway. Or, it could make a handling problem worse, depending on the set up of the car. Ie, if the car is loose, and the rears are a harder compound than the front, it will make it worse.