Yes... but variable from eMachine to eMachine. Many eMachines hard drives will work in a Dell without argument. In others, you need to use a Dell WXP Professional disk and boot to the disk, then run it in R for Repair Mode.
There are ways to tweak the drive, but too much to post here.
If it won't work, you will end up with a black screen... but the data is still there and the right boot disk will fix it.
The Dell 4600 used SP2, so you will be OK there, and many of the 4xxx series Dell Windows XP disks will work when you cold boot to the Dell disk, then go through the choices until you get to R for Repair (not R for Repair Console). If there, the R for Repair, will follow on the screens as you click through your choices AFTER R for Repair Console.
You WILL usually need to have to enter the 25 digit Dell product ID (usually from the sticker on the Dell case) available at the end of the repair install.
I don't think there is any option except to try it. The hard drive from the eMachines will not work anywhere else either... but if you have data on it, you can stick it into an external USB enclosure that you can buy for $15 to $30, the retrieve the data from a cleanly installed hard drive.
