If you absolutely must have a gold cannon in your town, and you can afford it, then sure, go for it. But as others have said it's definitely not necessary for completion of the event (in terms of getting enough bells) and it's only going to help slightly as far as the leaderboard goes (because you'll start being limited on elves to shoot if you go too fast). So it's not the most efficient use of donuts from a gameplay standpoint.
In another thread, I worked out that going from level 1 to level 20 with donuts alone would be around 12,000 donuts, or $400 at Gil deal prices. Obviously it will be less than that if you're starting from a higher level, but remember that the highest prices are at the top end, so starting at level 10 will not cut the price in half.
(If you only want the gold cannon and don't care about the bells or other gameplay effects from getting it sooner, then you should wait as long as you can before spending donuts, to make the most of the free cogs you get from elves and reduce the number of donuts required.)