I had stage 2 invasive ductal carcinoma. My critical illness policy paid out with no problem. I would be pretty sure that yours will too. The cancer does not have to have spread elsewhere for most policys to pay out. However, quite a lot of policies seem to exclude DCIS ie ductal carcinoma in situ, as this does not have the same potential to spread.
I would contact your insurer to see what the claims procedure is. Mine required a form from me consenting to them contacting my surgeon. Once they had a reply from her, I got the money in a matter of weeks. Good luck with this and with the rest of your treatment.