In short Brian, No. The CFA/Leagues state that games must be played with a referee in the ordered months. It basically says that a referee shall be nominated between the teams in the event of an appointed referee becoming unavailable in April/May (the end of the season).
The problem is (I'm told), there's a shortage of level 4 referee's in the county. Because of that, level fives are having to step up to the games the 4's are doing, the 6's are then having to take charge of the senior games that the 5's do, they then force the 7's up. There are plenty of level 6 & 7 referees, but they all get taken from the lower leagues and filtered upwards. One of my proposals at the League AGM is that where a referee is appointed to a match, in the event of him/her being reassigned, the game should go ahead with a nominated official from one of the clubs. If not, they get fined. I believe that's the rule for most leagues
There's a large number of games that should have been played during the summer, that didn't because the teams couldn't agree a referee. This paired together with the weather of late has amassed a huge fixture backlog. With no season extension either, the teams down here are up against it.
I'm afraid that's the impression I get on here sometimes