As far as I'm aware, if you are within the 12 month period where your American license is valid, you don't have to display L plates except when you take the practical test (you could argue during the test itself you have a fully valid license and don't require L plates but that might be a bit of an uphill battle!). I certainly didn't have any L plates on my car except when I took the test. I had a number of lessons which were obviously in the instructor's car so that had L plates on it.
In regards to provisional licenses, I believe you now need to send in certain identification to Swansea to get your provisional and then you can apply for a theory test. Once you pass that test you should be able to book a practical and so if you found a cancellation for the following week, let's say, you could take it. If I had to guess, most Americans who have moved to the UK take the test somewhere between 6-12 months of arriving if not later than that purely because of the move itself, and the time spent getting the provisional and taking the theory and practical tests and any ensuing failures that can often occur.
If I were you, I'd learn on a stick shift car. A vast majority of cars here are manual, you'll have a hard time renting an automatic if you ever needed to and if you ever had to drive a friend's car for whatever reason, it's more than likely to be a manual. Besides, they're much better than automatics!
You'll probably pick it up within a month's time, no problem, I bet.
Matt
