Does adding more letters provide added security compared to a standard substitution cipher? Let's say that a substitution cipher had 52 symbols instead of 26. For this, we would include all lower case and upper case letters. This creates a key space of 52! wehere the cipher text can contain both lowercase and uppercase letters. Would this provide more security to a standard substitution cipher?

I would say yes because it's an extra amount of symbols one would have to use and thus creating more options of how many keys can exist. However, I am doubtful because It's still just letters being used. Can anyone explain?
If I understand you correct you mean with "standard substitution cipher" one which has a mapping from one letter to a specific other letter with case being ignored (mapping 26 to 26). And your improved version would map one letter to another letter with case not being ignored (mapping 52 to 52). 

This would only be a very marginal improvement if at all. Given how words are structured (upper case almost only at the beginning) the necessary search space could be easily reduced to find out which target characters are mapped from lower case and which from upper case characters. The rest of the analysis can stay the same, i.e. looking for for characters and character combinations which are more common in the original language and mapping these to similar repetitions in the cipher text and thus quickly reversing the mapping.

In short: the system stays broken even if marginally improved.