Also since you asked the answer yes, it appears many people with T cells from previous coronavirus many time do have a pre existing natural immunity.
“Importantly, we detected SARS-CoV-2-reactive CD4+ T cells in ∼40%-60% of unexposed individuals, suggesting cross-reactive T cell recognition between circulating "common cold" coronaviruses and SARS-CoV-2.”
Also since you asked the answer yes, it appears many people with T cells from previous coronavirus many time do have a pre existing natural immunity.
“Importantly, we detected SARS-CoV-2-reactive CD4+ T cells in ∼40%-60% of unexposed individuals, suggesting cross-reactive T cell recognition between circulating "common cold" coronaviruses and SARS-CoV-2.”
https://pubmed.ncbi.nlm.nih.gov/32473127/
That's from 2020 Jun 25. Long before the Alpha, Beta, Gamma, Delta, and Omicron variants.
“People who had previously been infected with COVID-19 were better protected against the Delta variant “
The Delta variant is not currently a factor. See the 'Percentage of Cases Caused by Different Variants in Ontario' graph at https://covid19-sciencetable.ca/ontario-dashboard/