Tn welcome center Chattanooga

I can't answer your question about over nighting there, but if you are planning to head west on I-24 from there, beware that the exit for I-24 is on the left side of the expressway, less than 1/4 mile from the welcome center.

Depending on the time of day and traffic, it might make an interesting experience trying to get across, considering you are merging onto I-75 as people are entering the welcome center.