For a modified fuel injected Mini, it might help. If the mods increased airflow and the engine is now running too lean, increased fuel pressure can give the effect of larger fuel injectors, increasing fuelling and thus improving power.
The drawbacks are that unless the fuel pressure regulator is variable and can adjust to engine vacuum (a rarity) it may well overfuel the engine at lower throttle settings, killing off your fuel economy. FPRs that adjust to boost pressure are much more common and are a time-honored trick to get more fuel in to support a supercharged engine (and don't kill part-throttle economy because they don't raise the pressure when they don't sense turbo boost.)
I'm not sure that this trick would work on an SPI Mini - more experienced people would need to confirm. With just a single central injector, an SPI Mini is a lot like an electronic carburetor, and increasing fuelling at a central point might just make the fuel pool up in the manifold.
The trick does work on MPI minis, with the problems listed above (the original Cooper "90 hp" kits for the MPI had modified FPRs to supply the needed fuel.)
If the SPI is stock, the FPR IMHO would do nothing beneficial. If it actually helped a sick SPI Mini, it's probably covering up for some other failing in the system.
Dave