Not directly, AFAIK.
Here is the closest thing I came up with, under the assumption that my old Eclipse is recent enough so that it uses a similar form of update manager (P2).
In the old Eclipse, go to preferences->Install/Update->Available Software Sites.
Pick the ones that are not built in (you will see a name for them, or at least a non-eclipse URL). You can select the ones you want and then export them to XML.
Now go to the new Eclipse, go to the same preference window, and import the update sites from the XML. Now, when you install new software, you should see your update sites although you will probably still have to manually pick options for plugins that offer multiple downloads.
Important caveat: Some plugin vendors actually offer different update sites for different Eclipse versions, so you would still be pointing at the old plugin. This would typically happen if you never updated your existing plugin to a new version. One common example of this is with Subsclipse, so you may want to manually upgrade that one.