All the A series Canon cameras have an electro-mechanical shutter - when you push the shutter button you are just closing the contacts of a switch - well 2 switched really.
Switch 1 turns the meter on, switch 2 fires the shutter.
What actually happens when you "fire the shutter" (switch 2) is that the release magnet on the bottom of the camera opens, which releases the mirror box (which is spring loaded). In turn the mirror box mechanically releases the 1st shutter curtain once the mirror is out of the way.
The shutter timing is electronically controlled, with a second magnet releasing the 2nd shutter curtain when needed. When the shutter fully closes it mechanically triggers the mirror return mechanism and the mirror returns it to it's normal position.
The actual shutter release switch consists of 3 metal strips (made of fairly thick brass) spaced around 0.2mm apart.
However on a A1 you can get a sticky/rough feeling shutter release because of the actual design of the shutter release button on the top of the camera (the part you are actually pressing).
Under the shutter button (which unscrews) there is a pin which has a off-set round plate on top of it - this pin is what actually fires the shutter. This pin has a small amount of lubricant on it to prevent it sticking when being pushed by the shutter release button. Very occasionally the lubricant dries out and the pin becomes a little sticky..
You can also get a sticky feeling to the shutter button after servicing a camera if you do not screw the shutter button on just right when re-assembling the camera. There is no logical reason for this, and the cure is fairly simple - unscrew and re-screw on the shutter button. This seems to fix it...
I've probably serviced 50 or 60 A1's, and this happened to me maybe 10% of the time...
And Canon A series shutters are pretty reliable - when you hear a squeak you are actually hearing the mirror governor mechanism - the bearings are dry, and that causes the noise. These are one of the things you re-lubricate when doing a service..
So does a A series shutter cause camera shake? Im my experience no - if the camera is looked after, and serviced occasionally, then the shutter releases are smooth and they will not cause a problem..
Hope this answers your question