I will answer using the following definition of "qualified" -
Qualified: Having a solid knowledge of both the Bible and Watchtower doctrine, literate, strong public speaking ability, able to teach, able to keep confidential matters confidential, able to delegate workloads, general managerial skills, and the ability to give kind counsel on the previous mentioned items.
Answer: No.
The congregation I spent the most of my time in had at least 1 elder who could barely read or hold a conversation. It wasn't just his age. He was never on any committee of any type. He rarely had any parts on the meeting.
I also found it interesting that a lot of people in the congregation seemed to find out about confidential matters.
I also received a lot of anger from elders when it came to counselling. I don't mean I committed a minor or serious sin. I mean something as simple as not starting a song fast enough from the sound booth or being successful in tying in all the shut-ins on the phoneline.