Type Ia supernovae are heavily used tools in precision cosmology, yet we still are not certain what the progenitor systems are. General plausibility arguments suggest there is potential for identifying double degenerate Type Ia supernova progenitors in intermediate-age open star clusters. We present time-resolved high-resolution spectroscopy of two white dwarfs in the field of the open cluster NGC 6633 that had previously been identified as candidate double degenerates in the cluster. However, three hours of continuous observations of each candidate failed to detect any significant radial velocity variations at the > 10 km/s level, making it highly unlikely that either white dwarf is a double degenerate that will merge within a Hubble Time. The white dwarf LAWDS NGC 6633 4 has a radial velocity inconsistent with cluster membership at the 2.5 sigma level, while the radial velocity of LAWDS NGC 6633 7 is consistent with cluster membership. We conservatively conclude that LAWDS 7 is a viable massive double degenerate candidate, though unlikely to be a Type Ia progenitor. Astrometric data from GAIA will likely be needed to determine if either white dwarf is truly a cluster member.