It's covered in various threads, but in summary I'd say that yes, you'll see a significant increase in the quality of customer service when you have an enquiry - both with the phone being answered before it rings, and the ability to email BA directly with queries and (generally) get a very prompt response.
In my experience it makes a difference pre- and post-journey, rather than having any notable difference at the airport or in the air. (SS have said hello a couple of times, and that's it.)
I'm very happy with GGL - if you're a couple of hundred tier points off, it's worth the extra push.
Will leave you to use your own initiative to find the rest of the benefits -that's what the search function is for.