I realize this is an old thread, but I was looking for a solution and saw this post. The info here is not accurate. Also, if the OP is versed well enough to know how to use Microsoft Remote Desktop on multiple computers, I'm sure he/she is also capable of doing so with Apple Remote Desktop.
It is absolutely possible to use ARD over the Internet. It is also possible to do so with as many Apple computers on one network as you wish - whether it is over the Internet or from within your local network. All you would have to do is translate or map the port number you wish to connect to in your router. For instance, if you have 3 iMac computers at home and you want to connect to them while you are away from home and assuming you use port 5900 for ARD, do something like this:
(Substitute these IP addresses for the IP addresses that match your own equipment)
iMac 1: IP Address 192.168.1.2
iMac 2: IP Address 192.168.1.3
iMac 3: IP Address 192.168.1.4
Forward port 5901 to IP 192.168.1.2 and port 5900
Forward port 5902 to IP 192.168.1.3 and port 5900
Forward port 5903 to IP 192.168.1.4 and port 5900
Then in ARD, when you enter your IP address, follow it with a colon (:) followed by the port number matching the iMAC you want to connect to. For example, if your public IP address at home is 1.2.3.4 and you want to connect to iMac 2, you would use this for your IP address in ARD: 1.2.3.4:5902
Any modern router with port forwarding should be capable of doing this.