no .. there are a different set of adapters in between the fork and the brake caliper
a bigger disc uses a adapter.. to set it in the right place .

It's easier to see if you go into a bike shop and look at how the bikes are set up.

for the discs they come in 140 160, 180 and 210.

for street riding 2 160's will be fine . harder riding off road ,
and decending at high speeds then the discs that are bigger are chosen.

Hydraulic disc brakes are going to cost you more ..

since there is a seal around the piston to hold the oil in ,
there is little possibility of contaminating the oil,
with road grit and such.