Classical microwave drives are usually treated as ideal phase-coherent work sources for superconducting-qubit control. Here we ask whether the transverse field required for echo-refocused geometric Landau–Zener interferometry can instead be supplied by a finite precharged quantum source. We consider a single quantized bosonic mode coupled to a qubit through the Jaynes–Cummings interaction. The mode supplies the transverse coupling and its phase reference, while the longitudinal detuning sweep and the midpoint qubit echo remain external controls. We benchmark the resulting full qubit–battery dynamics directly against the corresponding classical-drive protocol at the same nominal avoided-crossing gap. At finite mean photon number, photon-number-resolved gaps, echo-induced redistribution between neighboring excitation sectors, and dynamical back-action soften and distort the interferometric fringe. The classical-drive response is recovered as the coherent energy increases, with the leading gap-broadening contribution to the contrast deficit scaling inversely with the mean photon number. For the state families tested here, photon-number narrowing and first-order phase coherence compete: the coherent state gives the largest contrast at the original operating point, while mild squeezing produces small enhancements in restricted regimes that retain a strong phase reference. We give this phase-reference resource a direct work-theoretic interpretation through the energy extractable by a phase-matched displacement of the battery. Geometric Landau–Zener interferometry therefore provides an operational benchmark of whether energy stored in a finite quantum source is available in a phase-coherent form useful for quantum control.