Unless there was some reason not to, and the customer understood, I always fired the gun as part of a safety check. For one thing, "safety" means more than "it won't blow up". A gun that looks good but won't fire may be very "unsafe" if it is to be used in a home defense or police/self defense role.
If I couldn't (bad weather, no ammo) or wouldn't (gun is unsafe) fire the gun, I advised the customer. I always checked headspace if I had the gauges; if not, I used the old paper sticker test to at least get a rough assurance against excess headspace.
I also checked for other problems, like a too-light or too-heavy trigger pull, tampering of one kind or another, proper operation, etc. What I did not check unless requested was whether the gun was sighted in or was accurate. I would do both if/when I had time but obviously at higher cost.
Jim