I don't think that's available as a Rover, but it is available as a One Day Ranger, and yes it's valid.
According to National Rail the ticket is called a "Hadrians Wall Country Line Day Ranger", this used to be known as the "Tyne Valley Day Ranger", and back in around 2005 this was cheaper than a Newcastle <> Carlisle CDR!
This is not a TOC-specific product.
The NRCoC allows for TOC-specific products in certain circumstances:
10. Tickets valid only in trains of particular Train Companies
The validity of a ticket may:
a) be restricted to; or
b) prohibit
travel in the trains of a particular Train Company or Train Companies.
Any such restriction or prohibition will be shown on the ticket. If you travel in a train with a ticket that is not valid, the relevant parts of Condition 2 or 4 will apply. If you are unable to use a ticket or any part of it, you may be able to claim a refund under Condition 26 or Condition 36.
This does not apply here.