Google recommends video site maps to help get videos indexed in Google. Their site maps follow basic site map protocol.
You say that SquareSpace does not seem to allow video site maps and then ask if not having one will be a deal breaker. The site map is helpful for search engines to identify videos, I'm not sure having one will affect your relationship with SquareSpace, but it will help your video's placement in the major search engines.
I've had good results using video sitemaps in the past and have never not used them, so don't know what the damage is. Working with Squarespace is new to me. I think I'm going to run a test - one with on a Wordpress site and one without on Squarespace to see if there's any significant difference in ranking and/or thumbnails showing up.