Vladimir,
Like Xander said, they're independent. I currently have ArcGIS Desktop 10.3.1 (ArcMap) and ArcGIS Pro 1.3. I use them both and both work fine. Like Neil said, make sure you have the memory! Pro likes to make my machine sound like it's about to go into orbit...
I am not sure the advantage of pairing them like Dan said. I have elected to keep 10.3.1 since I have had very little problems with it. I use Pro 1.3 for it's newer abilities (which some have been implemented into 10.4 and 10.4.1 but I have not upgraded my ArcMap - maybe I will soon...).