This is a question we wrestled with in the Nova Scotia committee that I was part of. One of the realities in modern communications, of course, is that it's not bound by electoral districts. To say you have to limit government advertising in the district and in the surrounding districts is kind of meaningless.
As you know, we have a ban on government advertising during an election, and the country doesn't seem to fall apart. I can see no reason why banning it during a by-election—of course, unless it was an emergency or a pressing matter—would be harmful to the public good. In fact, it would aid in ensuring full transparency.