Screen tearing would most likely occur when your graphics card is rendering more frames than what your monitor can show. For example: your RX 480 rendering 75fps but your monitor is only 60Hz.
If you get a 144Hz monitor, but your graphics card only renders less than 144fps, those adaptive sync techs (FreeSync/G-Sync) synchronizes your monitors refresh rate to match what your graphics card can output. However, there are some issues when the graphics output is relatively low to what the minimum refresh rate of the monitor can display (stuttering).
The RX 480 is best for 1080p/60Hz Ultra settings gaming. If you are looking at 1080p/144fps Ultra, I would suggest the GTX 1070 (or even a GTX 1080, depending on your in-game settings and the actual games you play).