The short answer is yes.
My experience isn't with anything like F-150s, but in general there are a number of suspension members whose job it is to locate the wheel in the wheel well. In doing this they set and preserve your alignment. These suspension members get connected to the frame/sub-frame and the knuckle in various ways, often bushings and ball joints.
If a bushing or ball joint is blown, something is isn't supposed to move will be allowed to move. This can be something annoying but not dangerous such as suddenly you feel a wheel out of balance no matter how many times you have it balanced or a light vibration on braking from run out or deposits that would normally be below the threshold of being felt. It can also be as dangerous as having the wheel alignment suddenly change dramatically as soon as any decent force is exerted.
Brake pistons, calipers, lines and other fixed parts aren't going to cause an out-of-round type of rotational shaking. Wheel bearings, rotors, and other parts that are spinning can, and it can be amplified by blown bushings and ball joints. A bad tire is unlikely to be glassy smooth when driving but shake you around as soon as you touch the brakes. A tire will usually vibrate any time it is spinning.
Yanking to one side could be a completely inoperative brake on one side but it's not usually violent - it would be in proportion to the amount of braking that you're applying, and I know there are lots of people out there with non-working calipers who can't tell. Yanking to one side can also be bushings, if a bushing collapses when the brakes are applied and causes one front wheel to change position.
With your combination of symptoms, I would definitely have all bushings and ball joints inspected. Ball joints can simply come apart when in bad enough shape, resulting in a front wheel suddenly going sideways and slamming up into the wheel well. I've seen a number of "street racer" Hondas sidelined this way where the owners were more concerned about light up washer jets than doing core maintenance.
If you don't know what you're looking for, take it somewhere. You could have an observer outside of the truck watch what happens when you brake hard from 5-10mph in a parking lot - look for fore/aft movement of both front wheels or anything else odd looking. Also listen for clunks.