Yes and no. Depends on your game style and expectations.
The cpu is all about fps. The gpu is all about eye-candy. So if your gaming style is open world, strategy, pretty much anything except fast motion games like first person shooters, then a 3060ti will feed you all the eye candy you can ask for and not affect fps.
However, if you are primarily fast motion, like first person shooters, car racing or anything that demands high fps, the 3060ti isn't going to be utilized much because the cpu just can't put out the fps to use it.
Your cpu upgrade path is very dependent on the motherboard. Most ppl who bought the r3 1200 did so because of budget reasons, meaning they also got an A320 motherboard, 8Gb of 2133MHz ram because that's the fastest speed the mobo would support back then and DDR4 was new and expensive compared to DDR3.