U2 looks like a PWM switching driver made for exactly this purpose. From the view of the supply it's a pulsing load with high switching currents, so should be thoroughly decoupled, although 0.1µF x2 (or is it one per IC) seems a little small. Are you sure one isn't larger? If not decoupled the high switching current spikes will go to the battery, and batteries don't like high ripple currents. It will shorten their life span significantly. The supply line will also form a loop current with the ground return, which acts as an inductor and antenna for emissions, which can be problematic and make the product fail emissions testing. Finally, the supply rail if the load isn't decoupled would ripple under the switching load, which means switching edges to the Q1 BJT (?) transition slower, increasing power dissipation in Q1.
Are you sure Q1 is a BJT and not a P-channel MOSFET? The latter would make more sense, but would also present higher switching currents.
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