Typically the hypervisor is run on bare-metal hardware for best performance.
Next one or more Guest Virtual Machines (VMs) are run on top of the hypervisor either automatically or manually. So yes you can setup a guest OS to autorun in seamless window mode (say Windows) and then another guest OS without any UI. You would need to do work so the user would not see anything unusual during boot but if this is a business perhaps you don't care.
Summary: Yes but you probally have much better methods to accomplish your goal. If we are talking about windows why not just a Windows Service that is seamless and in the background.