It can be done, but gramatically it is best to avoid it if possible. It not a case of starting a sentence with but and then having to leave the country out of embarrassment, however, there should be a mild amount of mocking.

Didnt go to the zoo today Matty, to busy studying The Analysis of Exchange Rates, The Analysis of Interest Rates, Monetary Policy, Financial Intermediaries, Personal Sector Finance, and various issues surrounding the forthcoming EU Enlargement, ready for my exam tomorrow.

Anyone want to swap...?