I don't think anyone's addressed this exact question.

As someone who actually is a member of BAEC I signed up - you get Gold instantly, the stays are for the bonus miles which appear on your Marriott account quickly, but BA doesn't currently seem to be transferring them through. I'm going to need to do some chasing, as this promotion has made me put through 14 days at a relatively expensive Marriott so far this month.

I doubt I'll be able to maintain Gold as I need to get back to Hilton properties to concentrate on covering my Miles n Points trip to Japan at the end of the year. Marriott have scored themselves a good shot at my custom for the coming year or two though, so we'll see!