Congratulation.
I would not send the PCC with the initial application for the same reason you've stated. AT least wait till you get your first communication from them, which for your batch most likely wont happen until after August when the form submission deadline is reached.
When they get in touch with you the first time with AOR, or additional document request link you application to the GCKey and start sending documents upfront if you have any.
PCC, medicals, etc. are time sensitive, you don't want to waste their validity while you're waiting to hear from IRCC.
The only exception to this is if you have already obtained the PCC for other reasons, otherwise dont spend time or effort on it now. Focus on the forms, its very intensive, make sure you fill it right, make no mistakes and provide all of the details and documents. Good luck.