Think of a geurgist as a combination of Magneto and Toph ^^
If one of them can do something with metal/earth, so can a geurgist. The only difference is the geurgist needs the alumen fuel in the first place in order to do it.
As far as drawing alumen from an item, it depends on what the alumen is doing. If it is in the object naturally, like how alumen naturally occurs in all earth & metal, then a geurgist couldn't withdraw particularly meaningful amounts readily, and the amount that they could draw wouldn't significantly affect the object's integrity. For example, a geurgist couldn't withdraw enough alumen from a steel sword to render it brittle or degraded, or take enough alumen from a iron gate to rend an opening in the bars.
However, in terms of alumen-wrought weapons and armor like alumail - a geurgist could easily withdraw that extra alumen, rendering it as little more than an impractical bathroom garment, and then use that siphoned caith to fuel more geurgy.
Does that help?