Quoting Sam I Am
Another benefit of course to doing it at home is that you aren't cutting into your holiday time while you're doing the studying of the book
That's a very good point, Sam.
One more drawback to doing a split training - depending on the length of time between your book/pool work (if the course is started in a pool, as mine was) and your real open water skill tests - you may be required to redo the simple stuff with the Thai instructors. The more time between the two, the more time to forget (and not practice) the basics. It could set you back a little, wasting more precious holiday time.
It basically comes down to whether you want to spend your time on vacation learning a new activity or being able to participate in it upon arrival. The learning can be just as much of an adventure as the participation. No matter what you decide to do, you'll love the end result!