Yes, it could but I'm guessing you guys have 10" brakes
, which cover a large range of wheel sizes (esp if there are brakes
on both axles, as some jurisdictions require). I think most of my cars only had 8" brakes (I could be wrong about that; it's been a while since I had a car).
I've found trailer brakes to usually be more than enough to lock up the wheels (typical starting point for adjusting brake controller).
I'd be checking carefully, of course, if I was putting 16" wheels on axle
with 7" brakes.