Hi, NE Nest,
Yes, the Photosynth embed code is just a standard HTML iframe element, so any site that allows you to post HTML unhindered should allow you to use the embed code.
When you're writing a new blog post in your SquareSpace dashboard, click on the little plus icon along the left side of your new post (under where it says 'Hello, World!') and scroll down to the 'Code' option. (It's in the 'More' category which is below 'Basic' and 'Commerce'.)
When the 'Edit Code' overlay opens, highlight the example paragraph and replace it by pasting the Photosynth embed code which you've copied.
When you're copying Photosynth's embed code, note that you can set options for:
1) whether you want the synth to load along with the rest of the page or wait to be clicked before loading
2) whether you want the synth to start playing as soon as it loads or wait to have the 'Play' icon clicked
3) how wide and tall you want the embed to be.