To the OP, how SL boots up and in what mode as default matters less. What you can do for sure is to run your application as a 32-bit app by going into "Get Info" and, if it's an option, check the "Open in 32-bit mode" box. That's the easiest way to try first.

The actually answer to what mode SL boots up as default is another matter. The quick answer is that it will try to run applications in 64-bit mode by default, regardless if SL is booting as 32-bit or 64-bit mode, strange as it may sound. It's pretty long story and you can read at your leisure later.