Doubtful.
The first advertised 4K chipset is the BCM7445. Nothing in Hopper's BCM7425 public specs implies support for HEVC/H265/HDMI2. 4K might be able to be squeezed out, but probably only using H264 encoding which isn't really practical.
The 7445 (family) is a pretty major architecture change, going to an ARM based processor instead of the current MIPS. Much, much speedier chip, but likely a little more work to port the existing code than previous MIPS to MIPS upgrades.
I guess they could release something via an LG Virtual Joey like DTV does with it's Samsung RVU clients, but it wouldn't be the Hopper doing the rendering.
But I'd be happy to be proven wrong.