Would an old moon be covered with more meteoritic dust?

The short answer

No. Expectations of a thick lunar dust layer were based on an incorrect rate of meteoritic dust influx, which even some young-earth creationist organizations now disavow.

The longer answer

I. Prediction based on incorrect rate of meteoritic dust influx

An early calculation that predicted a deep dust layer on the moon was based on a speculative estimate of meteoritic dust influx, now known to have been incorrect. The actual influx of dust is considerably smaller, and consistent with the standard age of the moon given by science. (Ecker 1990:183).

II. Disavowal by some creationists

To its credit, the young-earth creationist organization Creation Ministries International has completely disavowed the moon-dust argument (CMI n.d.). Likewise, in an Answers in Genesis magazine, creationists Snelling and Rush conclude:

Calculations show that the amount of meteoritic dust in the surface dust layer, and that which trace element analyses have shown to be in the regolith, is consistent with the current meteoritic dust influx rate operating over the evolutionists’ timescale. While there are some unresolved problems with the evolutionists’ case, the moon dust argument, using uniformitarian assumptions to argue against an old age for the moon and the solar system, should for the present not be used by creationists. (Snelling and Rush 1993)

References

CMI. n.d. Arguments we think creationists should NOT use.
creation.com/arguments-we-think-creationists-should-not-use
. Spotted 21 Nov 2014.

Snelling AA and Rush DE. 1993. Moon dust and the age of the solar system. TJ 7(1):2-42.

Ecker R. 1990. Dictionary of Science and Creationism. Buffalo: Prometheus.