Should a sessional instructor applicant submit a teaching statement?
I'm giving this answer from the point of view of philosophy, in the USA. I'd say that you should include a teaching statement in the packet, unless you are specifically directed to include only the materials they explicitly ask for. Don't bother with a research statement or some of the other junk that comes in a tenure-track packet. But this is a teaching job, and if I'm reading the above correctly, you don't have any experience as the instructor of record. So, what I would try to do is to write a short (1 page) statement that shows a committee looking at your packet that you are ready to walk into your own classroom and do your thing. 

It is really hard to write a good teaching statement. It's going to be even harder without a lot of first-hand experience. Fortunately, there's no end of advice out there on the web. For example, this, and this are both helpful.