Though not a horrible idea, it will leak water. I have my main halyard exiting through the mast base as you describe. Quite a bit of water comes down the mast in the rain, and it will go through your hole and leak into the boat. Not a huge problem, but maybe not what you expect.

Also, you need to use care raising and lowering the mast so as not to pinch the cable.

:: Planning a masthead VHF antenna install to meet offshore
:: reqs.
::
:: We were planning to do the typical thing: wire leaves
:: base of mast above decks, runs through fitting seal to
:: get below decks. We were not crazy about drilling
:: through the deck, sealing the hole, adding the fitting
:: weight, a quick-disconnect etc.
::
:: It then occurred to me: Why not drill through the bottom
:: of the mast, and on through the step, and just have the
:: cable pass through that hole?
::
:: Then I'm removing material/weight instead of adding it,
:: everything stays sealed, no need for quick disconnect,
:: etc.
::
:: Could even drill from inside the boat up, so no need to
:: drop the mast.
::
:: Its this a horrible idea?
::

:: -dan