A planar world does not have the right topology for this to make a vast difference. The reason is that eventually transport costs become prohibitively high from the unexplored edge to the center; and as you travel outwards, you only get linearly more land but you have quadratically much land already settled.
So, most people are going to be in the settled zone in the middle, and they'll have all the competition for resources that anyone ever has.
The frontiers might be an especially exciting place (as they were during expansion of comparatively technologically advanced humans around the Earth), but the constraints will, overall, be not all that different from the Earth except for people living near the unexplored boundary.
Boundaries are disruptive things. A lot of research depends on having really well-established institutions. But in the U.S., which is about as young as you get on the Earth, it generally takes a minimum of 50-100 years to get robust institutions that generate technology (e.g. UC Berkeley, Stanford, Caltech, etc, in California became global powerhouses, but it took ~100 years after significant settlement in CA).
Also, there's quite a bit of technological advancement that happens precisely because of resource limitations.
So it's probably a bit of a net positive, but because the premise of effectively unlimited resources is wrong (due to travel times), it's likely to be a modest effect.