He certainly made an admission against interest, so the strategy you propose might be the only one with a chance of succeeding.  It's akin to the Ambien defense, and not every judge will buy it.  

But he could be going for that defense right off the first tee.  In that case it doesn't hurt as much to stipulate you were under the effect of prescribed meds.  Like you say, that's the heart of the defense.  The unexpected drug reaction creates its own mitigating circumstance.

A good friend had a very similar idiosyncratic reaction to a sleeping pill and another couple prescription meds.  Fortunately he was on foot rather than driving (consequently, no legal difficulties ensued), but he ended up miles from home in the wee hours, not knowing where he was or how he got there, slurring, staggering, emotionally labile -- for all the world as if grossly drunk.  But INVOLUNTARILY so.  

Woods will have to convince Hizzoner that's the pickle he was in.  I think he's got a decent chance.