For modern drives (SAS / SATA), HP's "Hot swap" and "Non-hot swap" drive designations refer to the type of drive caddy (** and controller) used, rather than anything particular about the drive. All SATA and SAS drives are electrically hotswappable. (For SCSI and IDE disks, there was a real difference - only SCA SCSI disks were hotswappable, nothing else was)
So, if you have the correct disk caddies already, you can physically and electrically put in third-party drives just fine.
Whether the controller in your DL180 G6 will support a 2TB drive or not is another question, and one I don't know the answer to. It may require specific firmware on the drives, for example. Sorry I can't help you there.
As a side point, I've seen a lot of issues with non-RE ("RAID Edition") class WD disks when used in hardware RAID controllers. The RE disks have a feature called Time-Limited Error Recovery (TLER) (datasheet for RE4 disk), which basically means the drive gives up a lot earlier when it encounters some errors. Without this reduced error timeout, the disk stalls for longer, which results in the array controller thinking the disk is having a problem and subsequently removing it from the array. Your mileage may vary on this point - but if you find that the disks are being ejected from their RAID set without any obvious reason, you might be seeing this issue.
Updated to add: I think I still wasn't clear in my comment. There is no physical or electrical reason why you can't use any non-HP SAS or SATA disks in this system, because all SAS and SATA disks are hot-swap anyway.
Even the HP "non-hot swap" disks are technically hot-swappable, however the disk controller or back-plane in the HP systems with NHS disks may not support hot-swapping.
So, barring an unforeseen controller/firmware limitation, you should be fine.