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There is no question you will lose the Radio/CD display portion of the HUD if you remove your factory radio. You will also lose your warning and door chimes along with the use of your steering wheel controls. There are a number of different modules available to help restore the chimes and you can get some aftermarket steering wheel control systems. There is nothing available to to restore the HUD funtion. It will continue to work with other vehicle systems (speedometer, etc) and there is no damage that will result.
Your car may set an diagnostic trouble code if it loses communication with the factory radio and you don't have an additional module to take over the chime function. This typically won't result in a malfunction indicator light appearing on your cluster though.
Here are some sites where you can research related aftermarket interface modules:
Others with more experience in the aftermarket end of things will likely jump in here with more solutions.