The hardware scrapes in at the minimum for Windows 2012 (1.6 GHz proc and the minimum is 1.5 GHz). The proc came out in '06 and went end of life (EoL) Q1 of '09. In all likely hood this server is at least 7 years old (ancient in server years). Windows 2012 won't even install, if it detects you don't have the minimum requirements. Personally, if you want used, I would consider picking up something a little newer off of eBay, before you make all this effort. A seven year old server is very old. It will definitely need more RAM (I would add at least 4 Gb). The hard drive space is pretty low by today's standards, but if he doesn't have much data, it will probably work.
The are a couple of reasons you don't want users running RDP sessions on your DC. The first one is security. You need to give users local login rights on the server in order to do this. This is a really big security hole. They would then also be able to open browsers and download bad things directly to the server, quite possibly giving strange people in eastern Europe and China direct access to your server (wasn't that a cute kitten video they just clicked on?). The second and probably most important reason is stability. A user running apps directly on the server can cause the server to lock up or crash. Remember, unlike a workstation, you can't just reboot it anytime you like. A server plays an important role in any business, even small ones. You need to make sure it is reliable and secure.
There is a way to offer Terminal Services without additional hardware and that is to take advantage of server virtualization. Windows Server 2012 Standard (not Essentials) grants you 2 virtual server licenses, in addition to the host license. With adequate hardware (the above would not be adequate), you can create a Hyper-V (or VMWare) host on the underlying hardware and virtualize your server and then a separate server for the Terminal Server role. This would meet best practices. There is additional CAL licensing required to run more than 2 users for Terminal Services. If you are going to virtualize and run Terminal Services, I would consider 16 Gb of RAM the minimum and would probably recommend more.
It wasn't mentioned, but it is also important if you are running Terminal Services, that you secure access to the Terminal Server. This can be done with most firewalls and Internet routers today, using an SSL or IPSEC VPN. If Dave is going to configure remote access, he should definitely get some help, to make sure it is properly secured. Adequate backups are also going to be a consideration and Dave should probably also consult someone about his requirements around that, as well.