I suppose it depends on exactly what happens at the point of merger or perhaps just before. We do know that there are double degenerate systems with a total mass well beyond the Chandrasekhar limit eg
Although we do not have good independent distance measurements, the tight correlation between redshift and Ia maximum brightness (after correction for the light curve shape) does not suggest two obvious populations.
A mix of single and double degenerate progenitors giving different luminosity supernovae could be problematic for cosmological models though as the ratio of single and double degenerate systems might be dependent on the look back time. This has been even used in an argument supporting the double degenerate model as being the dominant mechanism.