No. Ironically, you're probably not old enough. AIM predated any meaningful adoption of SMS in the US by a long time. In the 90s, I was one of the youngest to carry a cell phone (13) -- I wasn't rich either, just a nerd. In the mid to late 90s that was really the nadir of cheap cell phone deals, you could get a phone for a penny and the monthly service for $15-20 for month if you paid $0.15 per minute or so. No SMS though, the phone didn't even support it (That was an all analog AMPS phone - The next year I got a shitty CDMA phone, but still no SMS).

I didn't have a text capable phone until after 2000.

Meanwhile, AIM well I carried the same ID since 1994 or so.