Going multi-platform may have had a minor effect on development and more specifically development time, but from everything I've read about the development of FFXIII it sounds like they lacked any form of vision, focus or leadership for long periods topped off with poor inter-department communication. None of those things can be blamed on the 360. In fact, they didn't really have an idea of where the game was going until they made the demo. This article does a pretty good job of painting a picture of the development cycle:
To be honest, the best thing Square Enix has done this gen is to buy Eidos.