It depends on which problem tab you selected. They have a priority scale with the ones that they try to answer same day, and then others that are answered a week later because they have low priority.

The number of support enquiries likely increase during big sales, so it is entirely possible that the sale does "get in the way of getting some customer support". Not to the level of "you don't get a response at all", but very likely to "it might take a little longer than usual".