Possible, but every Tom, Chan and Sergei will then have a go at the open RDP port.
I have numerous port 3389 attacks every single day. It's closed on my firewall but attempting to connect to it will result in all traffic to the offending host being blocked even on ports which are normally open.
Yes you're correct, it is possible, that's why I suggested it.
Re the attacks due to the open port; any potential hacker would need to know your public IP address and that your 3389 port is open along with deciding you have anything worth sifting through on you LAN. Quite unlikely in reality. If you have multiple attacks as you suggest, I'd suggest you have a much bigger issue to worry about!
Re TeamViewer; it does work very well as eckiedoo suggests. I use it from my Android tablet and Android phone if I don't have a device capable of RDP.
Having the target device powered up is really a non-issue. I never leave my server running, but use it in a 'on demand' fashion. I use a wake on WAN tool that I downloaded from the Windows store on my Win 8 tablet to wake the server as and when. Or an app called WOL - wake on LAN on my Android devices. Again, you will need to open up the an appropriate port on your router and enable WOL on the target's NIC but, it's extremely simple to do and you only need to do it once.
As has been suggested, we don't have a full understanding of what the OP is trying to achieve though.
Paul
Edited by deleted (Thu 14-Aug-14 22:35:00)