Can a dimmer switch be on the same circuit as outlets (with some of those being GFCI)? I've seen questions where the outlet was wired on the load side of the dimmer switch, but is this the same if the supply line is split before the dimmer? Will the outlets experience pulsing in this case too?
Yes. As all devices are connected in parallel there's no relationship between the switch and the outlets. In fact, You'd be lucky to find a dimmer switch that isn't on the same circuit as some outlets. It's quite common.
You're correct that it's not legal or safe to use the dimmer to control the outlets, though. That can lead to low-voltage/high-current conditions and device failure or fire.