.ps1 are associated with notepad by design, to prevent inadvertent runs like you can with .bat, .cmd. It's a risk management thing. You can change that via the normal file explorer way, but don't.
If you are saying, you want drag and drop .bat, .cmd on to a PS host and expect it to run, then no, PS will not do this. It is not designed for that. You have to call cmd.exe from PS to run .bat, .cmd files.
You can also add the PS shortcut to your SendTo folder. right click your script, select Sendto, and select the PS shortcut you created, or you can hack the registry to add PS the File Explorer main right click menu and avoid the SendTo step, but that is far more work.
Either way, this is not out of the box, and you are going to have to create something to pop the ps exe to run a script auto-magically once you drop or send something to it.
You can natively, drag and drop a file natively PS console or ISE script pane as long as they are started using the current user identity. In the console then just hit enter, in the ISE hit F5 (or click the big green button).