Possibly.

Most ISPs assign public IPs to consumers via DHCP. This can be totally random (and unlikely to be any logs although not impossible) and is generally the case with dial-up and ADSL. Alternatively, they can assign IPs via DHCP based on the MAC address of the modem (common with cable broadband) . If so, they are probably quite likely to keep records.

ISPs record who received what IP and when (if DHCP). They have been for years. (in the US anyway) Even as far back as dial-up..