Short answer is Yes, but with a catch.
There is a data transfer cable which will allow you to copy over everything from your 20GB HDD to your new elite 120GB HDD. This is a one-time only action as it formats the 120GB drive deleting anything that is on it before the transfer.
Alternatively you can re-download Live games onto your new HDD since they are linked to your gamertag.
The catch is that XBLA games record the specific HDD they were originally downloaded onto. If you download them onto a second HDD (your 120GB) they are not on the original HDD, and can only be played when you are connected to Live. If you want to play xbla offline, then you will have to keep them on the original HDD. You can re-download to your original HDD whenever you want, as it is still the same serial number, its just when you try to do it on another drive.
If you are always connected to Live then it isn't a problem, but you should be aware of this before trying it.
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