Is this enough accuracy for hunting deer out to 200 yards?
No quite honestly it isn't. You really need to beg, borrow or steal a better rest. You really need to know what the gun and load can do without you being so much a part of the picture. But the bad part is that rest is likely better than you'll have in the field so that means you likely will not be able to do as well when actually hunting.
It sounds like you've not done much shooting in quite a long time and perhaps have never been a very regular shooter. That's the case with a LOT of folks who go afield for big game each year. Too often at public ranges I've run into folks who have a hard time keeping their shots on an 8.5"x11" or even 10"x13" target sheet from the bench. That really is NOT acceptable accuracy to go afield IF you expect shots at or over 100 yards.
Your rifle might be a good deal of the problem. I'd first have it thoroughtly cleaned by yourself or a gunsmith. It needs ALL the copper removed, likely it is coppered up pretty badly. I'd take the scope, base and rings off and remount them making certain all is solidly mounted in the process. What kinda scope does it have? Do you have another you can try on it to see if that's the problem?
First do all the above and put same scope back on and see if it's better. If not can you get someone you know to be a good shot to try it?
How well have you shot this gun and/or other guns in the past? BTW some Remington semiautos will shoot an inch at 100 with ammo they like. You certainly should be able to get 2" groups with it at 100 yards if all is right.
You really must know what the gun/load is capable of so you can know what you have to work with. Field accuracy is not going to be as good as bench accuracy even using the pillow you are for a rest. It will only get worse.
As to how good is good enough, well the kill zone of a deer is about 8" or at most 10" and the range doesn't matter. So if you can't keeep the shots inside say an 8" circle at any given range you are not ready to hunt at that range. And that's from field positions NOT from the bench. From the bench I want 100 yard groups to be 2" or less if I'm gonna take the gun out to hunt with it assuming any shots over 100 yards are possible. Better feels good but honestly isn't required.