Mitch the Interview Puppet said you can record 4K UHD from the GH4 via the YAGH unit's four SDI outputs. Each output delivers 1/4 of the UHD (3840x2160) frame. This is also why UHD is also known as "Quad-HD."
So, yes, apparently, the 7Q can record GH4 UHD.

For our 7Q, it costs $800 over the basic hardware price to purchase the license to record 4K on our FS700.

We have two FS-700s and two 7Q's.

Be aware that you can record 1080p ProRes out of the box but that it will cost you an additional $800 to buy the license to record 4K.

Also be aware that you have to buy Convergent Design-exclusive SSDs. Won't accept regular off-the-shelf SSDs as the SSDs need a little handle on their top to pull them out of the recorder. You will need to RAID two SSDs in order to capture 4K RAW.

The 7Q also will only record 4096x2160. It cannot record quad-HD 3840x2160.

Finally, you will also have to buy a battery holder with proprietary plug that attaches to the unit's back if you want to make it portable.

For the purchase price, you get the recorder/monitor and an AC adapter. Nothing else. You will need much more at much more cost.

Monitor is beautiful; sharp and bright. Unit is very thin and lightweight. Focus assist is wonderful.