The answer depends on a few things...
Do you own them? Depending on your platform, the person or company who created the recording could own it. Or there may be a license. If you own the greeting, there should be no reason you can't retain it.
Can you access your greetings? If you have no access to the greetings, teh company you are moving away from might not be interested in helping you access these files, but there is still hope! There is often a way for us to extract the greetings but depending on the complexity and number of greetings there may be a fee. If there are chances in the structure you want to use there may not be a good reason to go to the effort.
But we can certainly discuss it and will as we look at creating the design for your new system (which is included as part of our setup process).