No, not all m.2 slots accept all "m.2" drives.
Yours, however...does.
https://www.gigabyte.com/Motherboard/GA-Z170-Gaming-K3-rev-10#sp
1 x M.2 connector (Socket 3, M key, type 2242/2260/2280/22110 SATA and PCIe x4/x2/x1 SSD support)
It will take either an NVMe drive OR a SATA drive, both in the m.2 format.
The one you've chosen will work.
But if you're just looking for faster boot time...that is not a magical solution.
For instance...boot time
A regular HDD may be 60 seconds
A SATA III SSD may be 30 seconds
An NVMe drive may be 25 seconds.
"boot time" is a total of the drive/OS doing its thing, AND the BIOS.
From the above time examples, the BIOS might be 15 seconds.
So....
15 secs of BIOS, then 45 secs of HDD booting up = 60 secs
or
15 secs of BIOS, then 15 secs of SSD booting up = 30 secs
or
15 secs of BIOS, then 10 secs of NVMe booting up = 25 secs
The NVMe drive is significantly faster (30% faster) than the SATA SSD, but that is not reflected in the
overall time, due to the BIOS having to do its thing.