Yes, you can use a .243 on deer size game and down and expect good results. I'd keep it 250 yards or closer though.
Now to digress.
I have many different styles (action types, bolts, levers, semis) of rifles with overlapping calibers. A 243 is a good mate for a second one (same rifle) in 308 as they both can be had in a short action. For long action, I like 270s with a matching 30-06. For the most part, I also go at least one above and one below. A nice all around, do anything in this hemisphere battery in bolts would be (same rifles or very similar in stocks and sights/scopes, different calibers) 22LR (or 22 mag), .223, insert either combo of above, and a 375 H&H. Knowing how to reload for each (sans the 22) to build an accurate cartridge for each and as a cost savings is a major plus.