I would then like to map a drive to an SMB share and perform operations on the files. This would primarily be counting the files and display this on the LCD screen I have on the Ardunio, but other operations might be useful.
The Arduino is not a full-fledged PC that might handle ultra-complex network file systems. Forget about using an Arduino for such stuff. A Raspberry Pi might do what you try to achieve, the included Linux operating system is able to handle SMB shares (as well as other network file systems).