realistically, yes.
But you can be missing out on other benefits. The use of EF-S lenses for wider angles, being one, and secondly, an UWA lens on FF becomes a wide-medium lens on crop. The "wideness" is wasted.
HoppyUK (a member here) can explain more about the advantages of EF-S lenses for wide angles on crop sensors.
If you put the same lens on a full frame and a crop camera, I think that it will pretty much always look a lot better on full frame. The image is just 2.5x bigger, the magnification is lower, the lens is working 2.5x less hard to deliver the same level of sharpness and it's got 2.5x the area to do it with. So the sensor is working less hard also to gather plenty of photons. There will probably be more pixels too, but that's less important.
That's the advantage of full frame - bigger is better. Simple as. There are a few factors at play apart from the lens, but they all compound one on top of the other to deliver much better image quality.
Just on the lens side, what is certainly true is that the centre will always look a lot better on full frame, if only because it doesn't have to find as much resolution at the lower magnification, so contrast and 'punch/pop' is greater.
The edges are a different question because they have never been seen before on a cropper - that's the bit that's been cropped out. So if it's a rubbish lens with poor edge sharpness that's going to show. But I think that the standard of optics we're probably talking about here will have pretty good performance right across the frame, so the edges too will also look good.
It's a complicated question that invloves a lot of variables, including focal length and f/number and image circle etc etc, but the bottom line is, if you compare like for like as best you can, full frame will win comfortably - often spectacularly so.
That's what happened to me when I went to try a new 7D against my old 40D, and pretty much by accidenct also tried the same lens on a 5D2. I had to look hard to see the improvement on the 7D vs 40D, but the 5D2 (with roughly the same pixel count as a 7D) was just miles better. Effortlessly wonderful quality. It was like comparing 35mm film to medium format, which for those that remember was absolutely no contest at all.
You do need a big print to really see the benefit though, and of course full frame costs more.