Yes you can. I do as the old paint, especially if it's poly, serves as a good smooth base. When you remove the old finish completely, you'll have to seal the wood. If you just shoot primer, it will get fuzzy, grainy and the wood will soak up a lot of primer. Save yourself the grief, sand and prime. I let the primer dry at least a day and if the sanding scratches show up, I'll sand smooth with 400, wipe clean and shoot the color. Here's a Strat I did, short cut as I used a special sealer that I shoot over 'soft' to bond the top coat. You can just use primer and go...
Strat refinish