Whether or not you can be competitive - and in fact fast as hell - with gamepads, or not, has already been positively answered: by those demonstrating that they are.
However, the feeling is totally different from using pedals and a FFB wheel, and so is the immersion.
Also, gamepad control is not the same like gamepad control. Using the mini-joysticks , the cursor keys, or PS4's motion control, are three very different things. The motion control in GT Sports work very well, btw. I was absolutely surprised by how well it works.
But a racing simulation without wheel is like a dogfight simulator flown via keyboard only: you get time passing a bit faster, yes - but does it really make sense regarding simulating the experience? I think not.
AC and RR user here, with Fanatec CSL Elite PS4 and CSPv3.