You are correct in your assumptions.
Your BB speed would increase quite a bit due to the star-wiring present and the connection of the 'bell-wire' (on T3 terminals) dragging the current speed down. TBH, if you booked a BB low-speed visit, the work
should be carried out for free under the 'normilisation of wiring' process. Plus, the 'exchange side' wiring should legally only be touched by Openreach.
What the engineer would do
, would be to separate the two cables held together by the white insulating tape, find out which one was carrying the Exchange conditions (-50Vdc / Dial Tone), and then connect this wire to the back-plate of the proper NTE5. The remaining cable along with the other cat cable would then be terminated on the front-plate of the NTE5. With an SSFP fitted between the two plates, this ensures that the extension sockets will still work for PSTN only services (Dial tone in other words). The Broadband signal will only present itself at the SSFP port.
All that said, if you have audible noise on the circuit now, there's a chance you could still have it after the re-hashing of your circuit ?/ That's why it may be better to request a proper BB engineering visit through your ISP ?? Your choice
.
PS ...... welcome to the forums.