If more of their locations were paired with Blaze like their test store in Lafayette, there may be more reason to go inside and have a glass of moscato with pulled chicken or a harvest ale with their carnitas.

But, I would imagine someone who's seeking authentic carnitas and knows how to pair their beverages with their food would seek other sources for them, not White Castle.
Most people heading to WC don't see it as a destination to hang out and spend extra money, just someplace to get cheap food quickly, at lunch time or on the way back from the bar. And then there was Valentines Day.
If they elect to expand this concept it will only be in select areas, and they would stop serving alcohol around 2:00 like everyone else, but what a pain for the employees. They're not paid enough to serve the prebar crowd and then deal with the post bar customers in the drive thru. I hope they keep their employees safety and sanity in mind if they run with this idea.