I'd suggest checking out this thread over on the Org, and check out the "Link to Website with data analysis":
Now, it would've been great to have a fully controlled study of every CPU using the same version of X-Plane, same clean installation with no addons, same operating system, etc... But, of course, with so many users, that wasn't possible. So it's very difficult to say how your 3770k setup will perform. And I wasn't able to find results for a 3770k in that link. However, a comparable i7-3820 at 3.6 GHz scored 84 in the FPS1 test, but it is not clear if that result used Vulkan, if the installation was clean, etc...
However, I was able to do controlled studies (in triplicate) and compare my old rig (i7 4770k at 4.4 GHz, GTX 1080Ti, 32 GB 1866 MHz DDR3 Corsair Vengeance 9-10-9-27) to my new rig (i9 10900k at 5.1 GHz, GTX 1080Ti, 32 GB 3600 MHz DDR4 Trident Z Neo 16-16-16-36) using Windows 10 and a vanilla (no addons, mods, etc...) copy of X-Plane 11.50 Final. Here are my topline results for FPS1 test:
4770k at 4.4 GHz in Vulkan: 124
10900k at 5.1 GHz in OpenGL: 165
10900k at 5.1 GHz in Vulkan: 200
10900k at 5.2 GHz in Vulkan: 204
This shows, at least at a very basic level, the considerable jump that results from an architectural change along with DDR4, a comparison between OpenGL and Vulkan using the same CPU and how far ahead these results are from older CPUs like a 3770k.
In short, you might be OK running that 3770k at 3.5 GHz with lower graphics/CPU-heavy settings and no VR.
However, if you really want to experience X-Plane 11 and the upcoming X-Plane 12 (and any other flight sim) in its full glory, I would recommend stepping WAY WAY up to the 12700k ($390) and a good DDR4 motherboard such as the MSI Pro Z690-A DDR4 ($220). DDR5 isn't worth it yet, so save your money and upgrade that GPU if/when you can find one.
Hope this helps