How much acoustic string buzz is expected on electric guitar?

I get slight buzzing on a few of my strings (standard 9 gauge set) when playing unplugged. When plugged into an amp, I can't say in confidence I can actually hear an audible effect.
I recently had this guitar setup, so I wonder if this is possibly a real issue or does minimal acoustic buzzing is normal, at least as long it doesn't affect the sound while using an amp.

That is, I assume that by raising the action enough the buzzing will be gone, but perhaps it won't be "worth it"?