I tried and played my Dualshock 4 for Fallout 3, and It is possible to platinum this game while using this controller. I'm unsure about fallout new vegas, but it might be the same.
Edited: I forgot to mention something. There is a possible occurrence that your Dualshock 4 will stop working while playing; this happens because your controller got fully charged. In my experience, I couldn't find a solution to this hassle and bought a Dualshock 3.