Can a broken sway bar link cause vibration?

A broken sway bar link will not cause a vibration at high way speeds but is a safety hazard. Here is a link to show you how to replace the ones on your car with an diagram (below)

https://youtu.be/y5zN-7XTEto

Here is a guide that can help find the problem.

https://www.2carpros.com/articles/steering-wheel-shakes-when-accelerating-or-braking

Less common things include rust or scale that fell between a brake rotor and hub or between a rotor and wheel. A bent wheel is another possibility but that too should show up at lower speeds. A wheel wobble can be found with a dial indicator placed near the wheel lip. If that doesn't show up anything unusual, a warped brake rotor can cause a shimmy from forcing the brake caliper to slide back and forth once per each wheel revolution.

That warp is easy to machine into the rotor accidentally during routine brake service. That is also best checked on the car with a dial indicator. There will be an access hole in the hub the brake rotor mounts to. Round spots of rust build up on the back side of the rotors corresponding to those access holes. If the brake rotor is removed and reinstalled in a different orientation, that trapped rust will prevent the rotor and wheel from mounting sitting squarely on the hub.

Please let us know what you find.

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Sways and vibrations have two different causes with different things to check. Weak front springs will let the car sway more when cornering at higher speeds. You'll also find that the ride height is low. There are published specs. That list the places to measure for each car model. Worn or broken anti-sway bar links and bushings will allow the body to lean more than normal during high-speed turns. You won't notice a problem in city driving. Broken links usually make a clanking noise too, especially over bumps.

Wheel bearings rarely cause a vibration. Most commonly they make a buzzing noise like an airplane engine that increases in pitch with increases in road speed.

If you can get a feel for how fast the vibration is occurring, it might help to figure out the cause. If it occurs once per tire revolution, it's almost always tire, wheel, or brake-related. If it feels like it might be three times faster than tire rotation, suspect an inner cv joint housing. A weak or collapsed engine mount can let one end of the drive train sag and change the angle and length of the half shaft. That puts the inner cv joint's rollers in a different area within the housing so they may be running beyond their previous wear areas. Slight imperfections worn into the rolling surfaces cause the rollers to bind, especially under the load of acceleration. When the shafts can't change length freely, they push on the spindle and steering system. That isn't typically felt at lower speeds or when cruising at a steady speed.

If your alignment mechanic isn't solving the problem, take him along on a test drive so you can point out exactly what you're experiencing. Find out what other solutions he suggests.