Not really. The TMS9900 [1] used memory as registers and had a fairly compact instruction set. Yes, it does have registers, but only three (a program counter, a status register, and a pointer to the current "register set" in memory). At the time, it was regarded as a slow machine, probably because of all the memory-to-memory operations.
[1] https://en.wikipedia.org/wiki/Texas_Instruments_TMS9900