The rule of thumb that I've seen in the past for whom is or isn't a Companion is that they have to ride with The Doctor in the TARDIS at least twice. In "The Day of The Doctor", 11, 10, and the War Doctor all travel in the TARDIS together. Which means that each of them traveled with the other twice. So does that make The Doctor count as a Companion?
You can go much further back...to "The Three Doctors" when Troughton rode in Pertwee's TARDIS. I'm not sure Hartnell could really count as he was secluded in that "time bubble" elsewhere. Sincerely, Bill
No, they have equal claim on captainship in the TARDIS. Note how they entered technically Ten'S TARDIS and after glitching a bit it turned into Eleventh's and then he seemd to be in charge.
Ooohhh, damned good point. Clara was already a passenger (Mind you, one that the TARDIS put through test after test) when she directed The Doctor and Susan to our particular Type-40.
Although, it's still the Tenth Doctor who does the flying, since the Eleventh is on the phone with the UNIT fella. Although, why does the War Doctor just stand there watching? He could be helping fly the TARDIS.