Probably not but BT do have records of lines that have not been converted to NTE5. Of course you could just say they have their records crossed between the defunct line and the current one.
Yes, CW1308 is cheap and if strip all the old crap out back to that first box and put CW1308 in neatly it'll probably do wonders for your ADSL speed... (mainly due to the removal of the crap rather than cable type). It'll also look genuine to any BT bod that visits.