Yes, you get critical hits with Staves (and Scepters and Chakrams) as a Mage and gems, DIY sagecraft builds or other Crit bonuses will increase the Damage and/or Frequency of critical hits.
Generally speaking, esp. with Staves/Scepters, you will NOT get physical bonuses. You WILL get physical bonuses with Chakrams, my work-a-day Mage Weapon.
Piercing, Bleeding bonuses are a no-go for most Mage-specific weapons as well.
Keep in mind that as opposed instead of a Finesse-type or Might-type character your Sorcery-type character will be inflicting (most) critical hits with Magic. So be on the look out for items that give you a "X% Critical Hit Damage with Magic" or just plain "X% Chance to Critical"
But you will do better with a Stave if you focus on technique instead hoping for criticals during 'button mashing.' The Stave is best as a slow masher: When attacking a single big baddie it's better to pause between button hits. HIT-breathe-HIT-breathe-HIT-breathe and then a quick bam-bam-bam with your melee weapon of choice. After all, the Stave is to the mage as the greatsword and hammer are to the Tank. It's for finish work and one-on-one fights -- not thinning the ranks. You'll want chakrams and advanced spells (lightning storm) for that.