You can clear out the sidequests in a given village (say, Quarrymill in South Shroud, or Horizon in West Than) in between 30 and 60 minutes no problems. There are, quickly counting at the top of my head, somewhere around 30 villages of that type before heavensward.
Then there are of course quests that take longer - especially in Heavensward. The moogles in Churning Mists I think have 59 quests alone, which will take you two hours at the shortest even if you push them at max level.
Quest chains like Gullinkambi in Anyx Trine will also take a while - there's five quests in that chain and you can't do them simultanously.

Even all this considered, if you just keep at it clearing every quest before stormblood shouldn't be a problem.

(And for the record, of course this would leave time to do all the "real" (very airquotes) content as well.)