Since you don't specify which Precision model you have, it's impossible to know what the GPU configuration in that system is like, but either way, if the previous hard drive was set up on an identical Precision model except for the GPU, then yes it should boot fine, and you should not need to disable the GPU in order to install drivers or even use Safe Mode since the GPU is not a boot-critical device like a storage controller.  However, the Windows environment on the HD you install will very likely fall out of activation when installed into a completely new system.  If the new system has a product key for that same version of Windows, you should be able to just enter it in order to reactivate though.  Or if you're using Windows 10 and have your license associated with your Microsoft account, that would work too.  Otherwise, you may have problems there.