Er... sadly, the short answer is no. If the Python program is running as a Windows service, there are multiple complications here... so let me explain.
First, in order to even allow the service program itself to access the network, it'll have to be running under a user account that is allowed network access. The SYSTEM account is out (all network access is forbidden), but you could use the "NETWORK SERVICE" account (which, in a domain environment, is really the machine's domain account), or another actual user account.
But you're not going to be able to map a drive in the service account, because it is not loading the user profile stuff that includes the ability to "map" to a drive letter. (Well, technically, if the service is running a CMD batch file, that script can map a drive letter and use it, but then it will not be persistent for the next logon... but nevermind that.) Instead, anything the program wants to get on the network should be accessed via the UNC paths (like \SERVERNAME\SHARENAME).
Lastly, it is not possible to make a drive mapping work "for all users"--a mapped drive is unique to each user profile (even if it uses the same letter to point to the same server share). If you have multiple users logged into a machine (for example, on a Terminal Server, or with a user and a service running under another user account), they cannot share the mapped drive--each must get his own.
However, you can do something like this: Make a login script (or Group Policy, etc.) that maps the drive with the expected letter (let's say "M:" for example) to the server share (\server\share). If this script runs for every user upon login, they'll all have the same mapping. Then when your program-running-as-a-service needs to access that share, it'll have to use UNC paths (and a user account with appropriate privileges, of course).
Hope that helps!