Short answer: no. Hyper-V features are for hosting virtual machines (VMs). As far as I know, you cannot host hardware-accelerated VMs from a VM. Kind of by definition, VMs are hosted from a host. If Linux is your host, Hyper-V is not the host.
(I guess it is possible to emulate an entire VM using software, without hardware-acceleration, but this makes the VM incredibly slow so I wouldn't recommend this. This is also not the way Hyper-V works.)
VM acceleration features allow you to use your hardware more effectively inside a VM, e.g. they might let a VM directly access a GPU. They will not, however, turn a guest into a (hardware accelerated) host.
When you install Windows 8 Pro directly on the machine, then you can add Hyper-V features to turn it into a host for VMs. I am not familiar with the WP8 emulator, but it sounds like it needs the current OS to be a Hyper-V host so that the WP8 emulator can run as a VM.
You will probably need either
- to install Windows 8.1 Pro directly on your hardware and add Hyper-V features to host VMs;
- to install Windows Hyper-V Server (which is free and downloadable from Microsoft's website);
- to install the full Windows Server with Hyper-V role (not free).
I expect that the WP8 emulator cannot be installed in a guest VM by making use of a Hyper-V host in this setup.
Installing the WP8 emulator on a Windows 8 or Windows Server host shouldn't be much of a problem. However, the free Hyper-V Server might not be a practical solution for your case (unless you can install the WP8 emulator on the Hyper-V Server, which may be tricky since that is, in a sense, a stripped down version of Windows Server Core).
If/when you choose to use Hyper-V as your hypervisor (host for VMs) then you can of course also run other VMs, e.g. to run Linux. VirtualBox is also available for Windows, but I don't know if that works alongside a Hyper-V installation. Perhaps you could run your existing VMs also on a Windows VirtualBox.
Finally, I have not done this myself, but it should be possible install a dual-boot system with Windows 8.1 and Linux, so that you can alternate between which hypervisor to use. To me this always seemed like a less preferable solution, since then you cannot always run all your VMs (i.e. you cannot run your Hyper-V VM when you've booted into the Linux hypervisor). I'd prefer to pick one and stick with it for all VMs on that machine.