In theory it shouldn't: the scheduling and the uploads are done by two different jobs. The scheduler job reschedules itself for 1 minute later as soon as it started, then adds (# of threads) new upload jobs. Those jobs taking long does not delay the scheduler at all.

Of course, just because a job schedules itself to run in a minute, there is no guarantee it is actually picked in that timeframe, so this might just depend on how congested the job queue is. We'll have to try and see.