1. I would not buy an OEM no brand name motherboard that makes claims to support a cpu that may require a bios update without know the namebrand and web site where you can get the bios from to upgrade it.
2. Sure its "possible" the bios is already upgraded and will work fin with your 3rd gen cpu.. its "possible" the bios is up to par. but without a web site to refer to its a crap shoot.
3. close scrutiny of the board (and this is assuming the photos reflect the actual hardware you will be sent I found a "ZX-H61CM v1.31" but the cpu slot
A quick google of the number discovered reveals;
Quickly I find on Toms hardware web site someone like you that purchased it, and found out the hard way he needs a bios update to used it, and discovered there is no way to get it updated.
https://forums.tomshardware.com/threads/trying-to-upgrade-an-unknown-h61-mobo.3332722/
All in all its is LIKELY the bios has already been updated to support your 3770.
Would I buy it.. no I would not.
But would find a B75, Z77 or Q77 motherboard listed here on ebay : like this board for 20$ less than your offering:
ASUS B75M-A, LGA 1155, Intel Motherboard for 31$