Yes, you can fire the camera without film.

In general, your test with a film rangefinder/SLR would be to open the back, remove the lens, and cycle and test every selectable shutter speed.

You’re not going to be able to confirm if your 1/30 selection is actually 1/40 or 1/20. You may be able to run a timer for longer shutter speeds to test for accuracy...but even if they are accurate, there’s no guarantee that the shorter speeds are too.

Instead, look for proper function (as you noted, no stickiness).

Then, get a roll of film and test the camera. Figure out a perfect exposure of a subject using a meter or another camera and then roll through every shutter speed that you can on that subject. Keep notes of your frame and chosen speed. Then, check the negs.

You should have the same exposure all the way through. Look for anomalies. Pending the type of anomaly, you can figure out the problem.

If you really, really want to set up the camera to run properly, then get it serviced. You’re looking at ~$250 in the States, assuming just a CLA (more of replacement parts are needed).

For the Canonet Specifically, please see https://camerapedia.fandom.com/wiki/Canon_Canonet_QL_17_GIII

The shutter speeds can be manually set and should be for any testing. Do note the battery advice in the article:

It was designed to use the PX625 mercury battery, no longer available in the US. The circuitry in the camera holds up well against slightly higher voltages, so you can use a PX625A alkaline battery as a drop-in replacement, but you will find your exposures tend to be slightly off. Only the autoexposure system requires a battery, however. The mechanical shutter functions perfectly under manual settings with no battery whatsoever.