Dell R630 supported PCIe to NVMe (m.2) adapter and drive?

Does this drive simply being Dell OEM make it compatible with the R630?

Yes. But so too is nearly any NVMe drive and adapter. Causing the fans to ramp up isn't a problem with the NVMe adapter per se, it's the R630 seeing the addition of any PCIe card causing the fan speeds to ramp up. Suggested resolutions include updating the Lifecycle Controller firmware or making a trip to the Processor Power Management settings.

Does the brand of NVMe drive matter if the adapter itself is compatible?

It might matter, there's a LOT of brands. Most any should work. Since this is a server, odds are you want a brand that has a track record of performing dependably under server workloads for a long time. Anything that matches that criteria is going to work in your R630.

Also, you can't boot an R630 off an NVMe disk unless you spec the server with the 4-disk NVMe backplane. Workarounds include putting the boot loader on the SD vCard, the Internal Dual SD module (IDSDM), or any SATA/SAS disk. After the initial boot sequence, the boot loader can hand off to the OS on the NVMe.