i've wanted to do that trail for a long time now, though i would do it from the oregon border south to san francisco. i think you might have the wind at your back-ish more if you head north to south (not positive). i'm not sure when the most consistent (good) weather would be - maybe august or september?
if i did it, i'd probably not stick to full thru-hiker, connect-all-the-footsteps mode, but instead be liberal in hitch-hiking the longer (ca. 5+ miles) road walking sections, as there are some fairly long, and semi-dangerous ones on hwy 1. also it would be fun to try to "hitch-boat" across the river mouths.
resupply would be easy with all the little coastal towns, and finishing by crossing the golden gate bridge would a triumphant ending for sure.
if anyone is curious, there are maps, etc. at:
have a great trip!