Bitcoin-core will ignore (not treat as a potential new tip) the new block header until it has downloaded and verified all the transactions. But bitcoin-core is no longer even capable of mining so this has no impact.
In practice, most miners (more precisely- most hashpower) do not need to see any transactions before that start mining on top of a valid block header. Since they do not know the state of the mempool without the transactions, they mine a “minimal” block on top of the valid header-only block. A minimal block has only a coinbase transaction which gives the miner the reward.
You occasionally see these coinbase-only blocks get mined and they usually show up right after the previous block since the miners switch to mining full blocks as soon as they get and validate the transactions in the previous block so that they can collect fees.
Here is a realtime list of these minimal blocks:
https://blockchair.com/bitcoin/blocks?q=transaction_count(1)
If you zoom in the most recent one (at the time I write this answer), you can see that the minimal block was mined only 10 seconds after the previous block…
…the one before that was 9 seconds after the previous block…
…and the one before that was 19 seconds after the previous block…
Remember that, on average, there is about 10 minutes between consecutive blocks, so the fact that almost all minimal blocks happen to come in with solve times of less than 30 seconds to me is very strong evidence that this is what is happening.
Additionally, from a game theory perspective this makes sense. If you were a miner and you just received a solved block header – would you keep spending your hash power mining on the tip that you are almost certain will be obsolete in a few seconds? Remember, the fact that you have seen that head means that it has, on average, already been seen by half the network. It would be smarter to start mining on that new tip (with a minimal block) – especially since you know that whoever mined that block has extremely strong incentives to promptly propagate the associated transactions otherwise they will forfeit the reward.
After more than 10 years, I do not understand why this is such a controversial take and why bitcoin experts fail to acknowledge this. Maybe because it violates the bitcoin “pureness” myth?
Anyway, if you have a better explanation for what is going on with these clearly existing minimal blocks and also why miners would act in economically irrational ways in this situation, then I would love to hear it!
But to directly answer the question with this info in mind: eventually miners would likely timeout on the fork that has the incomplete block… but not necessarily. Remember that we do not know what the code inside eg an Antminer does in this case (but we do know that it definitely does NOT follow the bitcoin-core rules!). It might be unlikely, but I could imagine a scenario where a majority of the hashpower follows that fork and builds enough work on it that it becomes the de facto main chain – even with the incomplete block in it. Basically this could happen if, by luck, there were 3 or 4 minimal blocks in a row from miners who optimistically mine. This would be a crisis and I’m not sure the final outcome would be, but I think it is incorrect to say that this is strictly impossible.
