Hi; welcome to the forums!
This seems to depend on how you're picking the tickets up. According to thetrainline's website, you can uplift your tickets at any machine listed on the website (therefore, you should be able to get them). Remember to take your card and reference number! And, to confirm, the First Great Western ticket's site is operated using thetrainline technology.
I know how easy it is to make this mistake, however; I've done it in the past for uplifting at the ticket office. Thankfully, Glasgow Queen Street and Glasgow Central aren't as far away as London and Bristol!