Quantity matters. Both the size of the aerosol cloud generated from a cough/sneeze and the number and size of the droplets produced is reduced while wearing a mask.

Stopped completely? No. Reduced enough to be a useful measure in some circumstances? Yes.

If I were going out and genuinely worried about inhaling something, I'd skip surgical masks and N95 disposables and just wear a sealed half mask using P100 filters. They're way more comfortable than either of the disposables, and provide much better filtration. Since they use exhaust valves, they may not provide much protection to others from your own potential pathogens, although I would expect some droplet suppression simply from the redirection of any exhalation through a small valve.

If it's a fabric variety facemask, I bet it absorbs a lot of the droplets. Not perfect, probably better than a smooth plastic facemask.