Travel / Traveling with the stamp for karta pobytu [NEW]

My partner is Canadian and has received his passport stamp for his application, which could take another 10-11mos. How does it work of he wants to go to Canada in the new year to see his family whom he hasn't seen since beginning of August when he arrived in Poland. Some American told him that he traveled to the USA while waiting several times with no issue, but all the official websites are vague and make me uneasy that something bad would happen.

If anyone has any info that would be great, dziękuję