Adding a Delta reward flight to existing Virgin reward itin

Hi all

We have PE flights LHR-LAX and LAX-LHR Ideally we would be looking to return from LAS but availability is looking unlikely, if I were to book Delta for LAS-LAX a few hours before our flight to LHR is due to leave would they be able to add this as a connecting flight to the existing booking - just thinking if there was an issue with a delay?