Pendolinos have a relatively civilised bike space - it's just a decent sized storage area in the power car (Coach 'A') with some straps. You shouldn't have much trouble getting a tandem in there (other than getting it round the corner from the external door).
The main issue is that the external door requires a member of staff to open it. This is fine when boarding at Euston, where the driver will enter the train via that door, and similarly when they get off at the terminus. It's a bit more fraught when you get on at intermediate stations, or when heading South, where the driver will be at the other end of the train, and you'll need to track down a member of staff on the platform to unlock the door.
Once on the train, it's prudent to remind the train manager that you've got a bike to unload shortly before your stop. Sometimes they forget.
As staff usually check bike reservations before letting you on, unreserved bikes occupying the space aren't a problem.