Here is a question - if you chose a time lord does that automatically infer you are a a Gallifreyan? And does that furter mean since you are a Gallifreyan does that mean you have to take the Alien trait?
I would say "Yes and no". That would depend on your Campaign. If the Campaign allows for non-Gallifreyan timelords and timeladies then you wouldn't have to be a Gallifreyan to be a timelord, necessarily, or to have the Timelord trait.
But, I'd say being a Gallifreyan definitely would be a strong qualification for the Alien trait. Although they look human, Galligreyans are quite alien !
And does that furter mean since you are a Gallifreyan does that mean you have to take the Alien trait?
I'd say not, though the write-up of the trait itself does seem to suggest it. But it would seem quite expensive for a 'mere' gateway, when combined with the points you'd already have spent for Timelord. Certainly, in my game I'd rule it was unnecessary for timelord characters to acquire it unless they also wanted some of the cool alien powers it provides access to.
And, of course, for some empirical evidence ... The Doctor's pre-gen doesn't have the Alien trait
Given how much of a munchkin trait Time Lord is I always charge for the Alien trait if they want the Gallifrey traits (some of Time Lord is Gallifreyan, some of it is Time Lord in my rules). Its still an amazing deal [especially since it gives you access to "Experianced Time Lord"].