How different are molecule with same connectivity
In my experience, calculated parameters like topological indices are not viewed as significant if considered alone. It's a strategy for finding trends or correlations and, subsequently, candidates from  large volumes of chemical structures. Many studies will publish trends they find in a target chemical groups which are not meant to apply to every chemical group.

An example of how all these seemly useless data is useful - see the Merck Kaggle Challenge. 
https://www.kaggle.com/c/MerckActivity

http://blog.kaggle.com/2012/11/01/deep-learning-how-i-did-it-merck-1st-place-interview/

Statistical significance is harder to comment on. I work with between 8 and 20 million data points and the idea of how to define statistical significance is evolving in cheminformatics as it evolves in big data analytics. It gets much more complicated because standard methods, such as the t-test, fail.

NOTE
I just realized there might be some fundamental confusion. Mol files include atomic information as do most graph based chemical representations. They're stored as properties of the nodes. An algorithm can choose to use or ignore this information. Not all topological parameters ignore atomic information.