Coupled Arcana (Ex)
Whenever you spend a standard action, move action, or swift action to activate an arcane school power, bardic performance, bloodline power, hex, or magus arcana, you can also activate an ability that uses mythic power as a free action. The mythic ability you activate must require the same action type as the other ability you activated or faster (a swift action is faster than a move action, and a move action is faster than a standard action).
Looks like no. Coupled arcana has a specific list of abilities that work with it, and qinggong monk abilities are not on the list.