Nope. 2-strand twists don't "train" the hair to curl anymore than rollers do.
Any physical manipulation that doesn't include a specific chemical interaction with the hair, will not alter the basic structure of the hair permanently. The only thing that's being done when someone curls, braids or in some way bends
the hair strands, is strictly a temporary form of manipulation.
That said, one guess as to why someone could think 2STs "curl train": If the hair is kept in twists most of the time, some part of it is being protected from the elements and from handling, and there'll likely be less breakage and (likely) more growth will be retained.
That could result in healthier
hair that is both longer and more manageable. I recall how healthy my hair was after taking it out of braids I'd kept in for a couple months. It looked shinier and curlier than usual.
That said, I can't stand it anymore ... have to tell you: I loooooove that vid clip you have in your signature LOL It makes me laugh every time I see it