Can an untrue wheel cause up down jerks? I've noticed during a ride that the back wheel was giving me unpleasant up-down kicks (sort of like a weight was added on a section of the rim). I realised later that it had maybe 2-3 mm of left right wobble but the about of up down movement doesn't seem too significant (I should mention that I can only do visual inspections). 

Can this up-down kerk be caused by that left-right uneveness?
Yes.  It's possible.  Newly laced wheels often have "flat spots" where the rim is out of round.  Generally you round and dish the wheel before you start trueing it.  It's possible that the wheel has a flat spot that you are feeling.  

However, there are another possibilities to include bad tyre mounting, improperly secured wheel (axle), bad tyre and assorted drive train issues.  It may be best to have a mechanic or experienced home maintainer check it out.