As the Mk1, MkII Cond & MkIV Cond were all "omitted from Vocabulary" & never redesignated as No1s i would have to say no.
Mk1 SMLE
MkIII SMLE (No1 MkIII)
MkV SMLE
No1 MkVI
The MkII & MkIV SMLEs were conversions of the earlier LongLees to Mk1 pattern (MkII ConD) & MkIII pattern (MkIV ConD) ConD = Converted