Conventional subs cruise speed is somewhere around 5 knots while a battle group's cruise speed is more than 15 knots. A conventional sub's sprint speed may reach 20 knots, but it can only endure only 20 minutes before the batteries runs out and have to surface to snorkel in which it can be detected by surface radar.There is probably some truths to those incidents but the problem is when facts are incomplete then any conclusion can be clouded. Both incidents seem to imply that the sub was able to trail the carrier group. One of the reason why US subs are all nuclear powered is because conventional subs do not have the speed to keep up with a carrier group. How a Chinese conventional sub is able to trail a US carrier group is an issue I cannot reconcile with known facts. If the sub had simply lie in wait and was lucky to be in the pathway then it is possible but then the report of it successfully trailing would be incorrect. Do US carrier groups typically operate at speeds beyond conventional sub as a preventive operational maneuver I would not know.
So NO, a conventional sub Chinese or not can not trail a carrier battle group, BUT it can lay low and calculate the sea current and vector of the carrier group to slip in and out which really takes skill and knowledge with a little luck.
Japanese MSDF subs have been known to slip out of a carrier strike group during anti sub wars exercises using this technique after gaining kill marks.