Can a PWM with 1% resolution in a PID heater loop achieve better than 1% temperature accuracy?
It depends on the time constant of the load. A heated load will often respond in 10s of seconds. 

If you generate 30% PWM for one second, then 31% PWM for the next second, that will look like 30.5% averaged over several seconds.

Oven thermostats tend to operate a minute on, a minute off, and still achieve oven temperatures stable to single digits of C. A 1% PWM adjusted once per second could do several orders of magnitude better than that.