We compare two Type Ia supernova samples that are drawn from a spectroscopically confirmed Type Ia supernova sample: a host-selected sample in which SNe Ia are restricted to those that have a spectroscopic redshift from the host; and a broader, more traditional sample in which the redshift could come from either the SN or the host. The host-selected sample is representative of SN samples that will use the redshift of the host to infer the SN redshift, long after the SN has faded from view. We find that SNe Ia that are selected on the availability of a redshift from the host differ from SNe Ia that are from the broader sample. The former tend to be redder, have narrower light curves, live in more massive hosts, and tend to be at lower redshifts. We find that constraints on the equation of state of dark energy, w, and the matter density, ΩM, remain consistent between these two types of samples. Our results are important for ongoing and future supernova surveys, which unlike previous supernova surveys, will have limited real-time follow-up to spectroscopically classify the SNe they discover. Most of the redshifts in these surveys will come from the hosts.