This absolutely isn't the case with the PiStorm. The PiStorm is more equivalent of replacing the 68000 with a much faster CPU (let's say a 68040, which I think is an option, though the Pi can likely run a lot faster than any real 040). You have the option of also letting it provide extra RAM and various other extensions (a video card, a sound card, network-backed storage, ROMs). The amount that you replace/augment is up to you, personally I'd probably use it as a way of getting a CPU and RAM boost for productivity tasks and perhaps the small handful of games that actually run almost unplayably slowly on a stock ST(e). No matter what you do, your original RAM, keyboard, joystick/mice, MIDI ports, YM chip, blitter, DMA, FDD controller are all being used, you're still somewhat limited by the bus speed, this isn't at all the same as running an emulator.
I think if a person is open-minded enough to consider CPU upgrades, the PiStorm is an interesting proposition - that it uses a Pi makes it no less authentic than any other upgrade that chooses an FPGA as its base instead, it just makes it much cheaper and more accessible. Personally, I'm waiting for BadWolf's STE PiStorm board to reach fruition so I can install one more easily, but I'll definitely be investigating it in the future and hopefully coming on board!