I’m sorry, and I’ll quote and screenshot this for later, but I’ve had at least two instances where I was on a group, everyone joined the match while one of the teammates was sent back to the main menu with an “Error starting game, trying again”, with the “Play” button retitled as “Rejoin Match”, and clicking it doing nothing. The teammate was still grouped, but they never connected to the match, resulting on the match’s cancellation, and penalty to the teammate, requiring them to restart the game so they could access the “Play” menu. So no. Not even when the errors you specified happen Blizzard takes the blame.
EDIT: Also: