Will Thermalright Ultra 120 work on AM4?

[Columbo]

For all of you noobs to computer building. The Thermalright Ultra 120 was the original 120mm air cooler design (circa 2006/2007). I am getting old. So when you see the CoolerMaster 212's. Those are based on the Thermalright 120 design. I have a Xigmatek Gaia 1283 that is a 120mm design that looks much like the Thermalright Ultra 120. 

Anyhow here is the adapter for the Thermalright ULtra 120. https://www.amazon.com/Thermalright-100700553-TRUE-universal-BTK/dp/B00UN05Q6A/ref=sr_1_1?ie=UTF8&qid=1504276596&sr=8-1&keywords=thermalright

This adapter works on everything up to AM3+ according to the description. I have this adapter for another Ultra 120 on a kaby lake 4560 build. 

 

If this will work with AM4, I would be putting a budget build together. One of the R3's and I would like to know what the best value 120mm fan is for the heatsink. 

 

Last question is the 1200 clock for clock the same as a 1300x if both CPU's were OC'd to 3.9ghz?