An AFCI consists of a standard overload feature.

But it also includes two functions to "bad" wiring.

One is a leakage dection. It is similar to the GFCI function, but trips at 30 ma which is too high for personal safety. Where needed you still also need GFCI protection.

The other detects parrallel arcing.

With wiring without a grounding conductor the leakage test is not affective.

The parrallel arcing test is still affective.

Current code requires that AFCI breakers used to feed outlets in bedrooms for NEW CONSTRUCTION. The way that most areas interpretate that you don't need them if you just upgrade the service and panel. But you do if you run new circuit to a bedroom or add on a bedroom. And then only those specific circuits.

However, there are lots of questions about how affect ACFI in actually preventing fires and many locations don't require them at all.

Having the AFCI's does not hurt anything, but the system is not fully up to modern wiring practices.

Thank you for this piece of information. If I understand it correctly, I would still need to have GFCI outlets as protection.

So, my question really should have been "Can I wire GFCI outlets without a ground on a AFCI circuit?" I hope this makes sense?

Yes you can put GFCI's on ungrounded wiring.

In fact that is one of the ways allowed to replace ungrounded receptacles with grounding style (the the ground pin is left unconnected).

If you do that you need to mark the receptacel No Equipment Ground. Such labels come with the individual packed GFCI's

And little plug in GFCI testers won't work. However they are not any offical way of testing a GFCI anyway. Only the Test button on the front is a legal way to test them.