Not true per this info: /train/1526/664/1982. That being said, the Bhopal Shatabdi rake would be really overworked if it is using an exclusive one. It barely gets 30 minutes or so at HBB (just enough to do quick cleaning and loco reversal), and 6.30 hour turnaround at NDLS.
KLK Shatabdi, arrival: 21.40, departure: 07.40 (10 hour turnaround)
HBB Shatabdi, arrival: 23.30, departure: 06.00 (6.5 hour turnaround)
And...
more... that is assuming right time arrivals. OTOH, if RSA is established (if one doesn't exist between the two), a little over 8 hours for both rakes in NDLS.
This, of course, doesn't explain the same signboard or does not guarantee RSA between the two, but it is certainly a possibility. It is also possible that I didn't see signboards on individual coaches of HBB Shatabdi in December as there may have been RSA activity to address fog issue. Still, I think a total of 7 hour (0.5+6.5) round trip (less, considering delays) is insufficient, especially for a high speed train.