You can create a scheduled task to run it with. If you check "Run whether user is logged on or not", it will run hidden in background (there is a "Hidden" checkbox, but it is only to hide the task from the Task Scheduler user interface).
Alternatively, create a Windows service using NSSM or similar.
It is also possible to create a simple launcher script with WScript/VB that you can double click from Explorer, create shortcut for, add to StartUp etc, that will execute rclone normally as current user, but hidden. Simple and easy to use, but could be a bit too "naive", depending on your use case.. Example: Create a plain text file with extension .wsf, e.g. "RcloneMount.wsf", with the following content (edit in your specific rclone command line, of course):
<job>
<script language="VBScript">
Dim WshShell
Set WshShell = WScript.CreateObject("WScript.Shell")
Call WshShell.Run("rclone -with -some -options here", 0, False)
</script>
</job>