It is generally bad form to overrule the OS management of a core. It is not best practice and you will not see gains in performance in 99.9% of cases. Especially in a multicore GPU, for the purpose you are using it.
As it has been mentioned, once the thread is running on a core and it is only able to use one core it will stay there. The OS will not impede on its processing of that app unless the server is overloaded and processing backs up across ALL cores. Get a dual or quad core and have fun. It will be fine.
If all you are using it for is Minecraft and there is no other activity then don't worry about it.
You will ALWAYS get better performance out of the server than in your original design of a single core processor running everything.
Simply install the OS, install that app and be happy.