Almost any commercially sold aircraft checklist will include a “brake check” item to be completed after starting the engine but before taxiing out to the runway… I would almost be willing to bet you couldn’t find a checklist without this item.
On the surface it makes a lot of sense, check the brakes before going too far… Generally the item is briefed to cover the “what if” scenario for the brakes not working as advertised. In short, the aircraft should be steered away from objects (fences, other aircraft, vehicles, etc…) so that the aircraft can be shut down and hopefully roll to a stop without issue.
The only potential problem with this is when the briefing on non-standard braking action occurs. This is an item that should be briefed prior to starting the aircraft. Once the engine is running, it is possible that depending on the type of issue the aircraft will begin moving, in some nonstandard way, immediately. Depending on the exact issue, of course it is possible that the brakes will hold until pressure is released and then they will not be as effective when pressure is reapplied to the brake pedals/lever (depending on the model). Either way, this is an item worth covering during your pre-start briefing, especially during a flight instruction activity. You should have a clear course of action, think about where you could point the aircraft if you can’t stop it with brakes…
However, it is also possible that only one of the brakes may not be effective; chances are one brake will be less effective than the other or not effective at all. A lot of pilots only think about the “no brakes scenario,” many over look the partial brake scenarios…

Pilots should inspect the line, caliper and the ground for leaks and the signs of leaks… For low wing pilot, this means getting “down and dirty” to some extent…
This is something flight instructors should be instilling in pilots early in their training. Just like sumping the fuel or checking the control cable connections during the student’s preflight inspection of the airplane… Checking the brake lines for fluid leaks prior to boarding the aircraft is critical, often times an issue can be detected here that could prevent starting an aircraft which will move in an unpredicted way and thus cause trouble… Especially since many times aircraft are parked and positioned in close proximity to one another on the airport apron.
If a “mushy” brake is suspected while in flight (in preparation for landing, obviously the wheel brakes don’t have any affect in flight) or while taxiing/rolling out, it is critical to minimize the braking done. Pilots often rely on muscle memory. In the case of brakes, a pilot generally “muscle-remember” that applying even pressure on the two pedals will slow the aircraft in a straight line, even while watching the aircraft deviate to one side, this can be tough mindset for a pilot to overcome…
Remember, when in doubt to consult a mechanic. Often times, even if the suspicion turns out to be just that and not an actual problem, it can be a great learning experience for a pilot of any skill level.
-Fly Safe, @MTElia1B9