After some discussions with NESCardinality a couple of weeks ago, we decided that it was very possible to beat dragon warrior without casting a single spell. Your first realistic chance to win the game is at level 27, although the odds are slim. By the time you hit level 29, you are a strong favourite to beat DL2 without even having to use a single healmore!

I was able to prove this concept on an edited ROM of DW with experience requirements cut by 67% (i.e. 33% of the normal values), and a few days later I was able to complete a full run without casting a single spell.