Whether it will look good depends on the skill of the painter.

Interesting!

Watch a few youtube videos. This one was interesting because he tried various combinations of paints and determined that some look good some, well, terrible. So you'd want to test and practice before you attacked your vanity.

Here is another and another using different techniques and materials.

You won't do it. And if you hire an experienced skilled faux painter, it will have been cheaper to just buy the vanity that you want.

Jusst a thought: You might also consider applying veneer if the vanity surfaces are flat.

• White Oak Real Wood Veneer
• White Oak Real Wood Edgebanding