No, TestComplete has been running JScript 5.8 since version 9.2, at least. I don't have a version prior to that installed. They've probably always been using that version of JScript, but I have no proof of that.
To be fair, TestComplete has used Microsoft's JScript engine since they put out v2.20. 2.20 was back in 2006-2007, and they were dependent on Microssoft's engine. In TestComplete 7, AQA said they were now using their own JScript engine. I'm assuming they forked from the MS JScript engine, but I've never seen a feature that was in TestComplete that wasn't in the MS Engine.