Recent observations of Type Ia SNe at redshifts 0 < z < 1 reveal a progressive dimming which has been interpreted as evidence for a cosmological constant of \Omega _ { \Lambda } \sim 0.7 . An alternative explanation of the SN results is an open universe with \Omega _ { \Lambda } = 0 and the presence of \hbox to 0.0 pt { \lower 2.5 pt \hbox { $ \sim$ } } \raise 1.5 pt \hbox { $ > $ } 0.1 { \mu { % m } } dust grains with a mass density of \Omega _ { dust } \sim ( { few } ) \times 10 ^ { -5 } in the intergalactic ( IG ) medium . The same dust that dims the SNe absorbs the cosmic UV/optical background radiation around \sim 1 { \mu { m } } , and re-emits it at far infrared ( FIR ) wavelengths . Here we compare the FIR emission from IG dust with observations of the cosmic microwave ( CMB ) and cosmic far infrared backgrounds ( FIRB ) by the DIRBE/FIRAS instruments . We find that the emission would not lead to measurable distortion to the CMB , but would represent a substantial fraction ( \hbox to 0.0 pt { \lower 2.5 pt \hbox { $ \sim$ } } \raise 1.5 pt \hbox { $ > $ } 75 \% ) of the measured value of the FIRB in the 300 - 1000 { \mu { m } } range . This contribution would be marginally consistent with the present unresolved fraction of the observed FIRB in an open universe . However , we find that IG dust probably could not reconcile the standard \Omega = 1 CDM model with the SN observations , even if the necessary quantity of dust existed . Future observations able to reliably resolve the FIRB to a flux limit of \sim 0.5 mJy , along with a more precise measure of the coarse-grained FIRB , will provide a definitive test of the IG dust hypothesis in all cosmologies .