If the push was accidentally started with the brakes on, what will happen since these towbars don't have shearpins?
While it isn't desirable to try to push an airplane with the brakes set, nothing much happens if you try. Nothing moves, and the tow bar is so strong in straight compression/tension that it isn't likely to be damaged.

Problems are much more likely once momentum and moving tugs/airplanes get involved; that is when a sudden brake application is more likely to "break a towbar" (actually, a shear pin or coupling -- designed to let go before you damage the aircraft landing gear). But even that is a side-to-side failure mode, rather than pure compression.

To answer the edit to the question about "without shear pins": pushing straight back, same, nothing happens. If the aircraft applies brakes while being turned and the towbar can't break, then either the tug gets slammed to a halt, or else something gets damaged - probably at or near the point where the towbar connects to the aircraft. (Or possibly both happen.) That's bad... aircraft out of service, seriously expensive repairs, etc. Which is why shear pins ARE used in towbars. Repairing damaged towbars is far cheaper that repairing damaged aircraft.