You could, but the respective variance estimates would not be independent, as they are in the usual application of Levene's test. It is therefore unlikely that the resultant p-values would be accurate. As well, unless deviations from medians are used for spread estimates (instead of deviations from mean), Levene's test is overly sensitive to departures from normality.
Was there some reason that you wished to avoid the Mauchly test?
You could, but the respective variance estimates would not be independent, as they are in the usual application of Levene's test. It is therefore unlikely that the resultant p-values would be accurate. As well, unless deviations from medians are used for spread estimates (instead of deviations from mean), Levene's test is overly sensitive to departures from normality.
Was there some reason that you wished to avoid the Mauchly test?