readynas duo v2 disk failed ..

Short answer:  Yes.  The best way to do that is with power on.  Remove the drive and put in the replacement without powering down.  In the admin interface, you will see that the NAS recognized the old drive removal and new drive insertion, then started a RAID sync.

Longer details:  If it really is just the drive that failed, then the other drive likely has no issues that would cause it not to be able to RAID sync the new drive.  If you still have full access to your files and are just getting a "degraded volume" warning, than that's probably the case.  But the other drive is also very old and could fail during the RAID sync because it's a very drive-intensive process.  If that happens, you lose the volume.  So before you put in the new drive, make sure you have a current backup of all files.

If you don't currently still have access to your files, post back.  But your chances of recovery are limited.

The drive compatibility list for the Duo is way out of date -- don't even try to find a drive on it.  Many smaller drives are SMR technology, which is bad for RAID.  That includes the WD Red (but not Red Plus and Red Pro) which WD insists on still calling "RAID purposed". which it definitely is not.  You want a truly NAS-purposed drive like a Red Plus, Red Pro, or Seagate Ironwolf.  An enterprise drive is another option, but overkill for a Duo and usually louder and runs hotter.  Do not use a current desktop drive.  Even if it has a model number similar to one you have or is on the compatibility list, it's almost assured to be SMR, not CMR as you need.

At this point, don't power down or re-boot the NAS.  If you do and the NAS thinks the bad drive is now good (which often happens, depending on the nature of the failure), it's going to start a long RAID sync operation that's eventually going to fail but that you shouldn't interrupt.  If you must power down, remove the bad drive before you power up and leave it out.  Then insert the new drive when you have it with the power on.

If you actually have a V2, then you may want to consider a drive larger than 2TB.  You won't get any additional space now, but you will once you replace the other drive.  Given it's "really old" and the companion drive (likely the same age) has failed, you will likely want to replace it soon before it fails.

So why do I say "If you really have a V2"?  Netgear had some minor hardware changes with the original Duo (which we call a V1, though it's not officially labeled as such) and added "v2" (and even "v3") to the sticker on the rear or bottom of the NAS.  That is not a "V2" of Netgear documentation.  After those small changes, Netgear completely re-designed the Duo and called it a "Duo V2" -- an incredibly shortsighted and confusing choice.  That real V2 can handle drives >2TB.  The V1 cannot.  A real V2 can be identified by it being labeled "Duo V2" painted on the front of the unit.  RAIDar will also identify it as a "Duo V2", not just a "Duo".