Just got off the phone with them and yes they will extend your contract, I am not happy and put in a complaint.
I recontracted my BB and phone on the 12th June. Then got the email about BT Sport and downgraded on the 17th. Have rung customer options twice about what happens about the contract extension and got told two different things but in both cases I was told that my original contract end date is valid ie 11 June 2016 and it has not been extended by the downgrade.
I just contacted live chat who confirmed the 11 June 2016 end date and stated it is not affected by the downgrade to Lite I made on the 17th.
It would appear that for those who have recently recontracted their services and then downgraded there is no change to the original contract dates , which is what one of the the options team said. The other person said that the contract would be extended to the 17th but was surprised that the system still showed the 11th.
It is all very confusing and what actually happens doesn't seem to follow what Bt are saying.