I seem to be saying "not yet" a lot lately, but not yet. This is related to the gradual move toward making quantization more flexible. Besides per-function quantization, the ability to have other sources of quantization points besides locations within the loop itself. So when setting the Quantize parameter, in addition to the current subcycle/cycle/loop also have Sync Beat, Sync Bar, leader loop locations, etc.
I was about to say do that in a script with "wait host bar" but I see that's broken. Scripts are supposed to be able to wait on sync pulses as well as loop locations.
Your example though suggests a third way. When a loop is in Pause, it isn't moving so you can't wait for quantization points in that loop. It could be that in that state, some functions switch to behaving more like Synchronization than quantization. The effect is the same, but it would just be automatic with Start. You don't have to fiddle with quantization settings, just make it mean that if a loop is Stopped, then Start synchronizes with the Sync Source like Record does.
There is an old function related to this called Realign that got lost in the last round of synchronization redesign that was intended to help here too. What that does is bring the loop back into alignment with the sync source. There are lots of ways to knock a loop out of alignment, Stop is one, but also Speed, Reverse, LoopSwitch...What Realign used to do is wait for the sync source to reach the next beat/bar, then retrigger the loop so that it starts playing at the corresponding location.