Yes. The innate immunity active in unvaccinated individuals is by nature non-specific, and allows a variety of mutations to coincide in a given population. This is what we saw during the first year of the pandemic. The dominance of vocs did not begin occurring until last fall, when vaccine trials and rollouts were initiated on a large scale, placing selective pressure on the virus (see graphs in this clip: https://youtu.be/B_Z_ezKnCsc).
Geert explains selection pressure here, beginning at 34:45.
https://youtu.be/qP31cfD3YOY