A factory Remington .22-250 will have a slow twist, which will limit you to short light bullets (up to 55 grains ) that will be blown around by the wind quite a bit more than the 68, 75 or 80 grain target bullets that are available but which require a quicker twist barrel.
So, you'll be at the least disadvantage if you shoot at closer ranges - 500/600 in preference to 900/1000, and 300 in preference to 500&600.
With factory rifles you get what you get and while there's a big variation it is also likely that you will be dealing with a rifle that is less accurate than a full-on custom rifle. Rifle accuracy matters in all classes of competition, but its effect is more pronounced in disciplines where the rules of the game allow for extremely precise aiming. So in F-Class, there is a real and actual competitive disadvantage if you don't have an honest 1/2-MOA rifle, since the permitted gear (scopes, rests, rear bag) allow a good shooter to break each shot to better than 1/10th MOA precision. In fullbore target rifle, which is fired from the prone position off the elbows using a shooting jacket, sling and iron sights, you can be competitive with a rifle that shoots just under 1 MOA. And in matches that are fired standing (particularly if you suck at offhand shooting like I do!), you can be competitive with a bit less accuracy than fullbore TR needs.
If you like shooting beyond 100, prefer to shoot with a scope, and like or are willing to shoot standing, you might want to try shooting metallic silhouette. It is fired offhand at 200m, 300m, 400m and 500m, and is pretty challenging. I had an opportunity to try it once, and managed to knock down the rams at 500m a few times - talk about a thrilling shot to have made! Downsides that I can think of is that a .22-250 might not be able to knock the targets over so you'd really only be firing for fun and personal accomplishment (you'd be able to see and hear your hits), and I also don't know if there is much or for that matter any highpower rifle silhouette shooting done in Canada.