Can the referee cancel the goal in such case?

The referee can not change a decision after restarting the game, unless it's an offence according to Law 12.3. or the assistant has signaled prior to the restart. Luckily enough a red card for punching someone is covered by 12.3.

This means the referee can send the player off.

Law 5 Referee

Except as outlined in Law 12.3 and the VAR protocol, a disciplinary sanction may only be issued after play has restarted if another match official had identified and attempted to communicate the offence to the referee before play restarted; the restart associated with the sanction does not apply.

And you're right. The goal does count. This is covered by Law 12.4. and even 5.2. itself (as highlighted above).

If the ball is out of play, play is restarted according to the previous decision.

The ball was out of play in your case, so it's simple. The game was restarted with a throw-in, which led to a goal. This was completely legal and even sending off the scorer afterwards doesn't change anything.

It actually doesn't matter what the restart of the game is. This can be a kick-off, corner, throw-in, free kick,... anything.

If the ball is not in play at the time of an offence the restart will not change. This also counts for throw-ins. As long as the ball is not in play the throw will be re-taken, even after a brawl.

Law 12.4. is very clear in that matter:

4. RESTART OF PLAY AFTER FOULS AND MISCONDUCT

If the ball is out of play, play is restarted according to the previous decision.