The original AOL client shipped for DOS with Digital Research's GEM widget kit, it wouldn't surprise me if they used additional DR hardware and software on the backend (VAX anyone?). When I worked on the AOL project, I would see e-mails from AOL ops (from AOL screen names, no less!) about how they would take scary and unique sounding things like "access rotors" down, so I suspect that given how early the launch was, the backend was extremely bespoke simply because they were making things up as they went along in order to launch a new and unique thing.
It wouldn't surprise me one bit to learn that it ran on VAX, HP3000, AS/400 or perhaps something even older and larger. You didn't hear about horizontal scaling nearly as much back then, most scaling consisted of "buy a bigger computer."
If you read blog posts and the like from people involved in those projects (MSN Messenger and AIM/ICQ, specifically); the companies would take advantage of protocol updates or other scheduled downtime to failover to newer hardware. So I doubt they were ever stuck on any “obsolete hardware”.