Yes, but it won't be an easy ride.
I did that with OBA back in 2006, did the exams while out there. I'd done quite a bit of reading in advance, and had a like minded house where every evening we sat around hitting the books and asking each other questions - they were a good bunch and we all completed the course in 4-5 weeks.
But if you do it that way, you need to be very disciplined and hit the books constantly - then when not flying, get upstairs to the computers and go through the CD-ROMs/hit the books again. In the entire 5 weeks I was there, we all went out for a beer on only 2/3 occasions towards the end - otherwise it was studying.
Several of the subjects are really quite trivial, but several are not.
If I did it again, I would try and get as many exams done before I went, purely because it would reduce the workload when out there.
But if you have the right mindset, you can do it. It is NOT a holiday.
The people had issues with OBA when I was there all fell into the same trap - turned up not even knowing the exam requirements, took girlfriends/wives and wanted to spend some time being a tourist, or expected a structured daily 9-5 class environment, which it is not - it is self study, with the exception of excellent class based lectures on a Wed night (dunno if the same chap is still doing them (he's here somewhere), but they were great).
(Less great was the cycling back in the dark with a maglite in your mouth by way of bike light! [:])