It makes it more likely that they deal damage (don't miss) and that they non-reduced damage (don't graze). It does not directly improve their damage. A priest or a wizard who hits deals exactly the same damage as a fighter or rogue who hits. A priest that crits deals the same damage as a rogues crit.

Well, if by "dealing damage" you mean simply "the damage of a single blow" then yea. But over the course of the fight your priest will have much lower damage output, killing enemies slower, and, as consequence, increasing amount of damage taken and probability to get some special attack instead. Higher accuracy allows you to hit high deflection target more reliably, graze less and crit more - that directly translates in more damage-per-second.

But a priest should be close second with baby sneak attack. A fighter with 10 more accuracy is not likely to outperform that.

10 more accuracy means that the fighter has higher chance of scoring a crit where a priest has higher chance of just grazing an opponent, and much less chance of grazing (via both more accuracy and 'graze-to-hit' conversion'); moreso for high-deflection foes, i.e. where it really matters. And fighter's passive +26.5% damage (via Weapon Mastery) already offsets a lot of priest's 'baby sneak attack', even with bad rolling. Theoretical damage is ok till your priest misses (or grazes) an opponent on his first roll.

10 accuracy is HUGE in this game - check how there are talents that increase accuracy by 5/6, and still worth taking, even though you can have just 6 talents. And you can't disregard special class abilities when speaking about realistic damage dealt, of which priest has less damage-oriented ones than most other classes.

Priest can still be good at damage, but claiming that he's not only worse, but better than a fighter at dealing damage is simply untrue.