If you're not going to use a local keyboard and mouse, some computers will stop booting if they detect neither present. You should check out your BIOS to make sure that your server is not set to "halt" on those faults.
Assuming the PC's bios can be set to: Halt on error: NONE You should have little problem with the machine once it is setup properly.
One of the issues you face for setting it up is its IP configuration. Are you connecting to your network and the internet through a router? Do you want to be able to connect to either machine from other remote locations, or just one, which one? DHCP or Static IP?
Another issue is firewalling the remote PC.
One little misstep with either the IP configuration or the firewall via remote access and you are toast without an onsite presense, monitor and keyboard.
It is unlikely your laptop will serve as monitor, keyboard and mouse for the desktop machine.
It is possible the desktop machine, once properly configured will never need you to connect a monitor to it.
I've have an XP machine that's been in the closet for nearly 2 years, connect to it via RDC and haven't had a problem with it. I only had the monitor hooked up to install the operating system, although I do have a cheap keyboard sitting on top to get it to boot/reboot....