Yes, but realistically only for much older hardware. Usually such "counterfeit" systems are based around an FPGA, e.g. MiSTer. The advantage is the hardware itself doesn't violate IP laws since it's a generic FPGA, while the legally questionable "programing" to make it copy a console's architecture (e.g. an N64) can distributed through decentralized channels on the internet.
Sometimes you'll get a reverse engineered System on a Chip like the C64 Direct to TV, but only where there's little to no risk of getting sued.
With modern hardware your end product will almost certainly be more expensive than the real deal (if you're able to pull it off in the first place). The company whose hardware you're copying is also far more motivated to find and destroy you. Hacking the real hardware to run pirated games makes much more sense.