Their lower sales rate in Washington state would suggest that no, they wouldn't.  I knew quite a few people (even Amazonians) who didn't buy from Amazon due to that factor.  Given a high state sales tax (>8% in both WA and CA), it's the simple economics of a higher price.  Also, WA no longer has a shipping facility, so the convenience of buying online is occasionally outweighed by the delay of obtaining the goods.
Would Amazon sell as much stuff if they required California residents to pay tax?