A YES Vote Condemns England to Perpetual Conservative Rule?

In order to prove or disprove this statement we can take a look at the 18 UK General Election results since 1945. 

On only 4 occasions may the Scottish vote have made any difference.

1. The election of 1964 where Harold Wilson’s Labour Party came to power. Labour had only a majority of 4. The absence of Scotland would have meant that Labour would have become the major party in House of Commons but be short of an overall majority by 9 seats. Labour would still have been the party most likely to form a Government. 
2. The first election of 1974 the election result would have been different i.e. that the Conservatives would have been the largest party in the Westminster House of Commons as opposed to the Labour Party. However it is still possible that Labour would have formed a minority Government as Heath’s Conservatives had been so rejected by the electorate. 
3. The second election of 1974 would have been turned from a small Labour majority into a hung Parliament with Labour still being the largest party. It could be argued that this could have helped Scotland. It would have meant that the Conservatives may not have gotten rid of Edward Heath as leader at the time. They did as history tells with Margaret Thatcher becoming Conservative leader, leading to a lurch to the right, and who ultimately became Prime Minister in 1979. However we shall never know. 
4. The most recent election in 2010 would have been turned from a hung parliament into a Conservative majority.

So we can be assured that…

1. Scottish MPs since 1945 have never turned what would have been a Conservative Government into a Labour one. They have also not done the opposite.
2. On only 2 occasions since 1945 have Scottish Labour MPs given Labour a majority which they would not have had in England, Wales and Northern Ireland alone. Those are in 1964 and the second 1974 election. The 1964 Labour Government lasted under 2 years. The second 1974 Labour Government was propped up by the Liberals through the Lib Lab pact. Without Scottish Labour MPs but with Liberal support Harold Wilson would still have had a majority. 
3. On 1 occasion, in 2010 the presence of Scottish MPs has deprived the Conservatives of an overall majority. However the Government the UK ended up with was predominantly a Conservative one anyway, with a few Liberal Democrat policies thrown in for good measure. 
4. Therefore only in 6 years since 1945 have Scottish MPs had any real influence in the formation over the composition of the UK Government. 
5. The representation of Scotland in the UK House of Commons is also being reduced from 72 MPs in 1983 to 52 in 2015 meaning the likelihood of any future effect is also reduced.

So the answer to the question is a most definite no. Scotland becoming independent will not condemn England to perpetual Conservative rule unless England itself wants it.

References:-
http://www.electricscotland.com/history/scotland/election.htm
http://www.scottishelections.org.uk/scotland/

http://wingsoverscotland.com/why-labour-doesnt-need-scotland/