Asaf,
There's no way to get that info I'm afraid. You can catch the number of rows using a rowcount component and multiply that by the width of a row to work out the maximum number of bytes that would have been sent through and that probably gives you a good indication. Note that this is the MAXIMUM, it doesn't allow for (e.g.) DT_STR/DT_WSTR columns that are not filled up.
-Jamie