If you have the baseband data, then you can fold the signal twice:
1. once at the period of the noise diode - for this fold, the pulsar will simply add to the system equivalent flux density. In most cases, this is negligible.
2. once at the period of the pulsar - for this fold, the noise diode will add to the SEFD. If the noise diode is a small fraction of the SEFD, then this is also not a problem.