As keinabel stated, this is unfortunately not possible.

Here are the potential workaround approaches:

Links to Server & Network Paths

Links should be formatted like this:
<file://domain.server.com/directory>

(Some engines may require the link formatted with more slashes at the beginning:
<file:////domain.server.com/directory>
)

However, you need to add this note:
(Right-click > Copy link address, and paste it into Windows Explorer)

Result: file://domain.server.com/directory
(or file:////domain.server.com/directory)

If anyone knows or finds another method, please let me know.

For Paths with Spaces

You can either in your <> link replace spaces by %20 (like you should for ordinary []() links too).
Alternatively, the following approach also works:

[\\\\domain.server.com\share\folder\subfolder\My Folder](file://domain.server.com/share/folder/My%20Folder)

Result:
\\domain.server.com\share\folder\subfolder\My Folder ((Right-click > Copy link address, and paste it into Windows Explorer))

You have to test whether your Markdown engine also supports this form:
[\\\\domain.server.com\share\folder\subfolder\My Folder](//domain.server.com/share/folder/My Folder)