The short answer is "It's possible".
It's important to understand the circumstanced where this is possible:
1: If your shared network drives exist on a vulnerable server, and the server itself is infected
2: If the user context in which the infection is running has an established connection to a network resource, is authenticated at the time of infection, and permission to change it. As an example, a cryptomalware running in the context of "SYSTEM" -unless exploiting a vulnerability- should not be able to make changes to a network share that requires authentication, provided another user with write permissions is not already actively authenticated.
3: If fileshares are poorly implemented. As an example, a very antequated and dangerous method that I have seen in widespread use is throwing a script in the startup folder of a computer that both connects and authenticates to a fileshare. As a matter of principal, in Windows (and mostly anywhere else), automated tasks should only occur within the context of an authenticated session, and should never be initiated by a script that contains hardcoded credentials
A good rule of thumb to consider when thinking about cryptomalware or really any malware: If a given machine or session is indexing files for quick search on a resource, there is at the very least a risk of disclosure or destruction by a threat operating on that machine or session.