Technically not...
As per rule, no.. At port of entry, they never look at your I-485 receipts. They only look at your Advance Parole papers. If you are travelling more than once in the same validity period, it is more easy for you at POE since it has already verified and stamped previously (you can use the same old copy when you travelled first).
But it may be required while getting your boarding pass. If the clerk at Airline ticket counter is not knowledgeable enough about Advance Parole and if your Visa has already expired in the passport, then you may need to show I-485 receipts.
This is what exactly happend to me. I was travelling second time abroad in the same year and my Visa has already got expired, the clerk was reluctant to issue boarding pass based on Advance Parole copy. I showed the I-485 papers, then she consulted her boss and then issued boarding pass.
It is always better to have I-485 receipts carry with you. If not, that's Ok if you manage getting boarding pass