Around 1995, AOL client itself could use winsock and work over tcp. So you could dial into your local ISP , select Winsock or tcp or some option like that on the main login page and be in AOL, while still have the ability to launch other apps like Netscape or irc client. You didn't have to dial into AOL's number. I use to use AOL on the school network to chat with family or friends that hadn't discovered the wider internet yet.
Prior to that, no, you couldn't do that. Being dialed into AOL meant you were only connected to AOL. The email did have an internet gateway (since 1992), you could email people at other internet hosts, but you couldn't use regular internet software until that DLL came out.