I have heard that also. While I can't verify that fact, I do know that drywall dust is too fine for standard vacuum filters and will destroy the motor. I would suspect that ash would do the same, over time. I believe you can "upgrade" your filter bag, and that should eliminate the worry.

i use my shop vac when i clean it out for summer. i put 2 of the dry filters on and suck it up. this is the only time that i clean out the FP with a vac. i like to leave a little ash in there when it is in use. plus, mine burns most every day during winter, went thru 6 cords last year, so i almost always have hot coals in it!

which reminds me, if you are going to vacuum it make SURE there are no colas hiding in the ash!

I don't think using a shop vac would be a good idea. Fireplace ashes are too fine as rustywillyz said, and a regular vacuum motor will become damaged sooner or later. Another thing to consider is that the hot ashes may cause damage to the hose, filters and cylinder. I would say the best solution would be to use an ash vacuum that has been designed for this purpose with fire retardant filters, a reinforced aluminum hose and a metal cylinder.

Here is a link that might be useful: Ash vacs reviews