Would a stationary WWII fighter fall on its nose with full throttle and brakes on?
(Wikimedia; arrows and CG icon are my additions) P-47 side drawing.

The thrust has a bigger moment arm around the tires contact points compared to the weight. It won't nose over below a certain RPM (it will be specified in the training). Below that RPM:


The weight will counter the thrust
The propeller downwash will produce downward force on the horizontal stabilizer
Applied brakes will resist the rotation of the wheels (airframe rotating around wheels)


From a training video for the comparable big-engined F6F Hellcat, the narrator says:


  You can't gun this engine to full takeoff RPM and manifold pressure while holding the plane with the brakes, if you exceed 2,000 RPM the tail will lift and you risk nosing over.


Answer is yes it can happen.

Note: for comparison, the max RPM is 2,700 for the Hellcat.