It is possible to use a heavy weight silicon oil but it will start to leak - only slowly though.
I have been using 500,000 weight oil made by a company called Ultimate and distributed by Schumacher Racing. It was recommended by the MCD importer here in the UK as an alternative to using limited-slip diffs.
I no longer use a front limited-slip diff in any of my MCDs - I prefer to use the standard diffs filled with a heavy weight silicon oil. There is still plenty of front end traction and of course it the best bit is the cash saved in not having to buy limited-slip diffs for all of my cars!!!!!
The only thing to note is that the MCD limted-slip diff is stronger than the pre 2008 spec standard diffs.