It is unlikely. Check out the fees, it is clear that the Ordinals Attack is no longer a thing. They have not been able to congest the mempool enough to raise the fees with their spam attack. So there wouldn't be any kind of incentive for a miner to switch to a copycatcoin (which is what it would be if they forked bitcoin, something like bcash, bgold, bsilver,...). Even when the attack began and the spam was at maximum the incentive to switch to such a fork was not enough.

Not to mention that at the end of the day what is being referred to as BRC20 is NOT part of Bitcoin protocol so if they create a shitfork where the only purpose is to allow these "arbitrary data" to be injected into the chain, they would be competing with actual token creation platforms such as Ethereum. In other words such a fork would be dead before it begins because the only reason why gullible newbies even considered this garbage when it came out was because it was using the bitcoin chain and bitcoin name to advertise it self even though this was never a token!