Can someone in the IRR (11 years AD and 3 years IRR) continue doing no-pay drills to work towards a retirement?

Why not just join the Guard or Reserve? You're obviously looking for the 20-year retirement. Just sign up and earn it.

Yes. People are conflating a number of things here, but to answer your base question: Yes.
You can drill in a "points only" status to acquire points towards a "good year", of which one needs 20 to retire.

You (obviously) won't be paid for them, and they won't enlarge your retirement check significantly, but it will allow you to get to 20 "good years."

As a practical matter, until they change the policy (especially WRT correspondence courses), you would likely be better served by joining a unit. But it is doable. If you really wanted to go down this path, you could also look at becoming "affiliated" with an AC unit. This would probably give your greater flexibility.

See the following for current guidelines: https://www.hrc.army.mil/STAFF/Individual%20Ready%20Reserve%20Homepage

There is a status that is in-between IRR and (Troop Unit) TPU. It is called IMA for Individual Mobilized Augmentee. You will serve 15-30 days a year with an active duty unit and you then go back on reserve status. Because it is an active unit, you may be called up when the unit deploys. Each reservist obtains 15 points a year for being in the reserve system. Don't let your 11 years go, make the Army pay you retirement by completing your additional service.
Yes, you have more time to serve and I understand the pain involved, I have four mobilizations and three overseas deployments to all the fun dirt holes we love to complain about.
I had to make a similar decision after my company command. Now I have 30 years in the Reserve and I have a few months before I am in the Retired Reserve.