Not really. Because your emuNAND is also stored on the SD card but on another partition that you (usually) do not see in your file browser on your PC.
But maybe (don't quote me on this) you can indeed use your 4GB card, then do the steps to create an emuNAND on your new SD, then extract the emuNAND from the first SD and inject it to the new one using
emuNAND tool and copy all the files from the "regular" partition from the old SD to the new one. No idea if this works but on the other hand, I don't know why it wouldn't either.