Does 148837392 sound like a legitimate vin for a 1968 Karmen Ghia?

Yes

1 = Type 1

4 = Karmann Ghia

8 = 1968

469464 = sequence number

The 1968 model year spanned Ch# 148000001 thru 148999000 and 1968 models were built from August '67 thru July '68. There were 19,177 coupes and 4,157 convertibles built during this model year.