No. Currently the
users type does not return any
private_info and neither does the
user_timeline type return any voting information.
No other API method allows for detecting a user's vote history except one question at a time. You would have to fetch every single question and test the
downvoted and the
If you limited your search only to questions asked since the user's last visit you might be able to brute-force this for votes on new questions
(Even Stack Overflow only runs about 7.5K questions per day (Quota is 10K calls, max 100 Q's per call))
-- but I wouldn't recommend it.
And, you'd miss new votes on old, established questions.
Update: At least one script works around this and fetches voting history by scraping the: