Yes you can.
Though it's not very clever, as you would have to pay more to buy later one of his works.
If you're doing it just for the bonus connected to the promotion, you can. You should consider that you're helping players that already have invested in that artist.
You can't buy works from a celebrity (unless you have a commission).
There are lots of reasons that you might do this in addition to the $5 bonus. You might gain from a reputation tile. You might gain from the side effect of a "promotion" action (e.g. gain money based on visitors in your gallery). You might gain value from a work you win in the auction. You also block anyone else from buying work from this artist.