We have compiled the largest sample of multiwavelength spectral energy distributions (SEDs) of broad absorption line (BAL) quasars to date, from the radio to the X-ray. We present new Spitzer MIPS (24, 70, and 160 m) observations of 38 BAL quasars in addition to data from the literature and public archives. In general, the mid-infrared properties of BAL quasars are consistent with those of non-BAL quasars of comparable luminosity. In particular, the optical to mid-infrared luminosity ratios of the two populations are indistinguishable. We also measure or place upper limits on the contribution of star formation to the far-infrared power. Of 22 (57%) upper limits, seven quasars have sufficiently sensitive constraints to conclude that star formation likely contributes little (<20%) to their far-infrared power. The 17 BAL quasars (45%) with detected excess far-infrared emission likely host hyperluminous starbursts with L FIR; SF ¼ 10 13 Y10 14 L . Mid-infrared through X-ray composite BAL quasar SEDs are presented, incorporating all of the available photometry. Overall, we find no compelling evidence for inherent differences between the SEDs of BAL versus non-BAL quasars of comparable luminosity. Therefore a ''cocoon'' picture of a typical BAL quasar outflow whereby the wind covers a large fraction of the sky is not supported by the mid-infrared SED comparison with normal quasars, and the disk-wind paradigm with a typical radio-quiet quasar hosting a BAL region remains viable.