It would have to be in a round about way. Government attacks DC token project because it runs on Bitcoin, puts pressure on it to switch to a captured token like ETH.
If the DC project fees accounted for the majority of Bitcoin mining revenue, miners would have to choose between a compliant Bitcoin fork in order to keep receiving revenue from the project or loosing revenue.
That's not how DC works though. A successful project on DC might be vulnerable but not bitcoin. To miners and bitcoin its just another hash block. Blind merged minning is already bitcoin core by the way. Your premise requires miner censorship, which is not and has not been successful now despite years of attempts.
If you would read Pauls years of work on DC, you would see that DC actually increases security. More profits for miners secures the network, more... that's the way satoshi designed it. In addition, more miners entering the space means a larger physical lobby against gov interference (Matt Kratter).
If the a majority of Bitcoin miners revenue comes from a drive chain project, and that project demands a change to Bitcoin or it will go elsewhere. The miners are incentivise to move to a censorship fork to receive the revenue from the DT project
