Yes - CIC will almost certainly request an FBI PCC (they typically request one as soon as someone has been in the US 5 months or more). I would include one in your application rather than waiting for CIC to request it.
Hi, I have stayed in US for total 145 days in last 10 years. Any risk of been asked for USA PCC knowing people have bene asked when they stay about 5 months or more though rule is 6 months of more ? I am on border of 5 months.