Sorta—there was no direct video out from the cartridge on the SNES (though oddly enough, there were audio out pins), so the Super FX chip had to actually generate sprites on the fly for the PPU to composite together. This resulted in unfortunate color limitations.
You can see in the debug info for Star Fox 2 that the dynamically allocated sprite count was something that they had to constantly keep track of: https://r.mprd.se/fup/up/35454-Star_Fox_2_(Japan)_(Proto)_(A...
The DSP-1 was a preprogrammed microcontroller that preformed certain calculations that would have been inefficient to preform on the SNES CPU. The inputs were written to a memory mapped location, and the outputs read back. An interposed copier could simply redirect these reads and writes.
The SuperFX and SA1 used the cartridge's ROM and RAM for program and data, and therefore these enhancement chips are placed between the SNES bus and the cartridge memory. The cartridge memory is unavailable to the SNES bus while the enhancement chip is executing, as in the SuperFX, or the the enhancement chip enters wait states while the CPU is accessing the cartridge memory, as in the SA1.