Yes, it will. This diagram, however, is the current Holyrood chamber depicted as per party composition:
Scottish National Party (69)
Scottish Labour Party (37)
Scottish Conservative Party (15)
Scottish Liberal Democrats (5)
Scottish Green Party (2)
Independent (1)
The Tories got 13.91% of the Constituency vote and 12.4% of the Regional vote. They have 15 seats due to the electoral system, which they initially opposed. They have 3 Constituency seats. (Under FTPT, that would have been their likely total).
Even renamed, I don't see a very bright future for right of centre politics in Scotland.
I don't think that independence will "rid Scotland of Tories". It will, however, make it extremely unlikely that they would form a majority in the foreseeable future.