emails? no, those are typically archived by the provider or corporate mail host. even though you download them to your PC.
I don't know a single ISP who archives personal emails. While ISPs will back up whatever emails are left on their servers every day, they don't systematically archive every email that goes thru.
Corporate, yes, ISPs no.
Why do I know this ? I run services or consult to a bunch of companies in the ISP business.