The short answer is: Sometimes.
I had to file a missing dine request with PC RN earlier this year. Here is the timeline:
3/2 - Filed missing dine request
3/17 - Received boilerplate reply asking for documentation
3/17 - Emailed scanned copy of receipt as requested
4/16 - Received reply indicating that rewards for this restarurant are Sun-Fri and this dine was on a Sat
4/19 - Replied that the dine was actually on a Sunday

4/21 - Received reply indicated that info has been forward to Reward Claims department, allow up to a week for review and processing
5/4 - Dine posted and points credited (may have been pending for up to a week before that, of course)
More recently:
6/1 - Filed missing dine request
6/12 - Received boilerplate reply asking for documentation
6/13 - Emailed scanned copy of receipt as requested
6/15 - Received reply indicating that Rebate department has documents, allow 7-14 business days to post
7/6 - Dine posted and points credited (may have been pending for up to a week before that, of course)
I also had a restaurant switcheroo eligible days of the week on me. I asked RN to confirm that the change had, indeed, happened before I dined, and they claimed that it had, but who knows.
Give it another shot.