It depends on the PCIe adapter and/or the motherboard Bios whether your system can boot from it.
Either the motherboard supports PCIe storage devices on its own, in which case it will just work. (The Gigabyte web-site doesn't mention this capability, but that doesn't mean anything. It is often not mentioned in documentation at all. However, given its age, I would be very surprised if it can do it.)
Or the adapter can present an extension Bios to the motherboard Bios that adds the boot-functionality that the motherboard doesn't have on its own. (This particular adapter doesn't. Adapters that can do this are very rare and more expensive.)
Please note that your motherboard is PCIe v2.0. That means you will never get full performance from the NVMe SSD. (It still will be a bit faster than a SATA3 SSD though. Just not that much faster.)
I know see that you mention Win7.
I do hope you realize that Windows 7 is obsolete and out of support.
Getting Windows 7 itself to work in such a configuration is problematic all by itself as Windows 7 was never designed to do this.
Andrew Morton just metioned that in the comments as well.
In short: As data-disk it will certainly work (albeit not at full speed).
As boot-disk things get very complicated and may not be possible at all.
You seriously need to consider if it is worth it to buy an expensive adapter for this NVMe SSD.