Well…of course you can do it--you can do almost anything if you're willing to take the trouble, but it seems to me pretty pointless to use godmorgon in this situation. You'll definitely lose the whole top drawer and may have to lose a good part of the bottom drawer, too, because of the plumbing.

Godmorgon is very easy to adapt for vessel type sinks, but not so much for this. I'd honestly look for another brand that comes with an undermount sink already. This is going out of your way to make your life harder for less benefit. Personally, I wouldn't do godmorgon unless I was willing to use the ikea sinks meant for them.

This look is popular enough that you should have plenty to choose from. Check out Duravit--they used to have a lot of vanities in this style, although I haven't looked lately.

I am doing a wall mounted faucet, and almost every floating vanity I like (and can afford) has pre-drilled holes in the sink / countertop. What I like about the Godmorgon is that I can buy the vanity without the top.

BUT I am definitely open to other vanities. Do you have any suggestions?