It is possible. Such manufacturer could create HD wallet and publish its public key. Then, each device could have one of the child private keys. In this way, any miner using such equipment could use it to sign any message and prove that it has such equipment. For me, it seems pointless, but technically it is possible.

When solo mining, proving that particular equipment was used to mine a block is trivial, all that is needed is checking the coinbase transaction. When mining in pools, proving that is harder, because it is possible if miners will switch to Stratum v2 or similar protocols where they can control their blocks.