No, not much if we are talking of a handful of flowers per bush. Reblooming hydrangeas can react to the lower temperatures by producing new bloomage so, yes, they could produce new blooms quite late. A few old wood blooming hydrangeas also react like that but usually, it is a small number of blooms per plant.

I have some unnamed hydrangeas that bloom only in Spring but, once every few years, they will also produce blooms (1 or 2 total for the whole plant) from mid Oct thru early November, meaning before they go dormant in late November.

If the whole plants are exhibiting lots of bloomage then that could affect bloomage in Spring. In such a case, I would try to stop all amendments and fertilizers by the end of June in future years... to see if that helps make them go dormant.

Blooming should be fine on all of those. You will probably lose some stem that you will need to cut back mid-spring after new growth is fully underway. The ES plants are remontant and firelight supposedly will bloom from any buds that survive all the way down to the crown.