In "Deja Q," the human Q tries to take charge in Engineering, an attempt which greatly annoys Geordi. After Geordi tells Q to shut up, Q angrily states that he will not be spoken to in that manner. Geordi then calls for Data, who strongly suggests to Q that he cooperate.
It seems unlikely that Data would harm Q, so maybe he was suggesting that he'd physically drag Q from Engineering if the confrontations continued.
Yes, I think Data was implying he would physically move Q out of the engineering department by force.
Data will not injure somebody because of his moral programming, but he might injure them to prevent harm. He would not be interested in physically harming Q or overpowering him, but he would forcibly remove him from engineering if instructed by the chief engineer, Geordi.
Q was reduced to a human in that episode, so Data could have overpowered him. However, I doubt Data would need to move him by force because he has several means to move him without harming him.
The point is that Data had multiple means to detain Q without harming him, but would have if necessary. Merely by threatening force, one can compel another to change their behavior without actually using force.
I gotta say the crew was admirable in their professionalism towards a vulnerable and detested Q in that episode.
If by "hurt" you mean violently inflict physical punishment on Q, then no, as it is against the ethics code of Star Fleet to injure a prisoner without good cause, as well as the fact that Data (as an android) probably has some protocols that disallow him from harming a human unless he is in some special circumstance. But keep in mind that there are other ways to "hurt" someone. For a good part of that episode, Q was kept in the brig, which he was obviously unhappy with. He was also forced to wear clothing which "wasn't his colour".
Aside from physical punishment, there are plenty of ways in which Q could be dealt with, including sending him back to the brig or surrendering Q to the Calamarain (waiting outside to attack him). I don't think Data was threatening to physically assault Q, rather he was reminding Q that disciplinary actions could be taken if he continued to resist.
Data's statement could also have arisen from the general feeling of disdain that the crew had for Q, as he had constantly brought trouble for the Enterprise in the past (including alerting the Borg to their existence).
TLDR: Data was not making a physical threat, but rather reminding Q that there could be punishment for his actions.
I'd say he was suggesting he would physically remove Q to the brig, rather than threatening physical harm. The rest of the crew may have liked to see Q roughed up a bit, but this desire wouldn't have been a factor in Data's motivation.
Q is not dumb, and it may have been galling for Q to be reminded that cooperation opens more opportunities, and maintains existing opportunities.
Data's strong suggestion would have reminded Q of this, as in his human form other desires can overwhelm.
Data may have known that Q would respond intellectually to this reminder.
