You have to pull the drawer out.

I think it's great you are thinking outside the box. Folks often add pull outs under sinks for better access to cleaning products and drawers would have that function. However, I do think you would more quickly discover a water leak with the cabinet style versus drawers and a leak can do a lot of damage when undetected.

A pullout is probably a better choice. This is mine.

It isn't difficult to remove IKEA doors to access plumbing. You extend it completely, and then sort of lift at an angle and it will come off the glides and pop out. You'll get it after you assemble, because it's the opposite of what you do to install it.

Yes, drawers are far more functional. No, it's not less storage, because you still have to allow room for plumbing even if it's an open cabinet. A pullout provides the same storage, but with more work to open (open door one, open door two, then pull out, and then reverse it all to close), so I don't see a benefit there. Plus, there is also the possibility that someone might bang the inside of the doors and damage them if they don't open them fully first. (The kitchen we ripped out had pullouts that were installed twenty-five years ago, and they had a lot of damage, despite being used only by an older adult couple.)

I'm assuming you're having a new kitchen installed. So, before you have the cabinet supplier build you this drawer/sink cabinet, consult with a plumber. Ask about hooking up/moving the plumbing as close to the back wall as possible. This will maximize the drawer depth. Your plumbing comes up through the floor or out from the wall. One may be easier than the other to move. Don't have cabinetry built on an assumption that it can be moved.