No, I don't drop my armor, my shield and my weapons.
Due to weapons breaking (more important with RQII than RQ III, I agree but it still occurs) and disarming rules, plus the fumbles tables and impaling, I usually start with 3 or 4 weapons on me, just to be able to finish the fight.
My current character has a ringmail armor (10 ENC), a broadsword (2 ENC), a hoplite shield (a scutum in fact, but ruleswise it is the same) (5 ENC), a kukri (0.5 ENC) and a dagger (0.5 ENC), plus 4 darts inside the scutum (2 ENC).
That means a minimum ENC of 20. I thus start at 5 (CON 13, STR 12).
I'm not counting a bow and a javelin (carried by my mount), nor the luggages and food (idem).
Runequestement votre,
Kloster