Yep fluid leaking from the rear seal of the master cylinder will fill the booster. Standard test is to stick a cable tie in through the vacuum port and see if it comes out wet. Brake fluid in the booster will eventually damage the rubber diaphragms and seals inside.
There are a few tests you can do on the booster.
If you hear hissing from the pedal area at any point in the pedal travel, is has a vac leak.
Unplug the vac hose with the car off, if the booster is holding vacuum like it should, air will rush in when it's removed.
With the hose unplugged and the car running, you should have good suction on the end of the hose.
With the car off, press the pedal, the first two or so presses should be a bit soft with longer travel, after that the travel should be shorter and harder, as the vacuum held in the booster is expended.
You can try driving it with the vacuum disconnected, and see if the brakes are worse than they already are. Be very careful obviously, they may in fact be significantly worse than they already are, if the booster is working.
You may have some seized caliper pistons, blocked brake hoses or other faults causing a lack of force being applied to the pads.