It does support remote connections, but at the NFS or SMB level.
Since only a single process may write to a database, it would be best if that process were local.
NFSv4 has built-in file locking, which is likely the most preferable protocol. SMBv2 is a massive rewrite of that protocol, and I expect any file locking problems would be addressed (especially as Microsoft sponsored SQLite changes specifically for Windows 10).
Remote readers in explicit read-only mode likely won't hurt, but there is a deeper discussion below.