Connect Gigya with the Twitter module

The Twitter module has the option to fetch the users timeline and display the tweets of all users. However, it would make no sense if a user creates an account using his Twittername via Gigya, that he has to add his Twitter account again to fetch his tweets.

Would it be possible to add a small glue module to the Gigya module that depends on the Twitter module? That if one connects his Twitter account using Gigya, his tweets can be displayed automatically?