Yes, there's definitely some degree natural immunity. There's mixed evidence as to whether it's stronger[0] or weaker[1] than full vaccination, but it's definitely better than nothing.
[0] https://pubmed.ncbi.nlm.nih.gov/34735425/
[1] https://www.medrxiv.org/content/10.1101/2021.09.12.21263461v...