Mattresses vary greatly in the materials used and how they are constructed.  The older, traditional style innerspring mattress consisted of a layer of felt over the springs and additional layer(s) of fiber padding, covered by a tightly-quilted, smooth-surface fabric cover.  If that's the kind of mattress you own, then cleaning it with a cannister powerhead or upright (or Kirby in hand-held mode) will work perfectly.  The only caution would be that if the cover fabric is a fine satin-type material it could be damaged by aggressively stiff whirling bristles.  When I was selling Kirbys we were cautioned to be careful and use our better judgement when demo-cleaning a mattress.  If the fabric looked at all fragile, we were to lift the belt and use suction only to be safe.

US made innerspring mattresses made in the last 10-15 years are almost universally (except for the cheapest ones) made to be "non-flip" meaning that there is only one side up.  Layers of foam now replace much of the fiber batting material under the surface fabric and that spongy cushioning will nullify most of the beating action of a powerhead.  The cover fabrics vary greatly now; everything from heavier, tightly woven material to fine sateen to terrycloth and jersey knit.  My mattress has a knit fabric cover and a powered brush would shred it instantly.  Thick plush and especially lofty pillowtop mattresses often have a highly convoluted, deeply tufted surface.  On that kind of mattress a nozzle of more than upholstery tool width would bridge over the deep tufts and the suction would be lost.  My mattress is probably the supreme example.  The only way to clean a mattress like mine is by using a small upholstery tool so as to maintain constant contact with the surface and rely on suction and airflow alone to remove whatever is embedded. 

The "sleep number" air-inflated mattresses are essentially the same except that in place of springs there are air bladders.  They have one slight advantage in that you can unzip the cover and clean or even replace the interior padding materials.  On the far end of the spectrum, and presenting a more unique cleaning challenge are mattresses made entirely of foam, either 100% laytex or the heat/pressure-sensitive viscoelastic (memory) foam. 

All of this is rather moot for me personally, since I keep my mattress encased in an allergen-proof cover to keep it clean. 

On a related note, there's a common misconception about dust mites.  The critters are invisible to the naked eye and are themselves completely harmless.  It's their feces that cause an allergic reaction in some people like myself.