No there is not a way to use Alexa to determine how many visitors a website has. If you don't have access to their log files or whichever analytics program they're using how do you expect any website to estimate traffic?
It's anyone's guess how much traffic a website receives. But unless you have access to their analytics or raw access logs you shouldn't assume any estimates are correct.
Who cares where they rank what if they are spending large amounts of money on TV ads in a particular city and getting lots of direct traffic. Would anyone be able to account for that? Or what about paid ads, or affiliate ads? How about referral traffic?
Don't even bother trying to figure it out or find a site that claims to have estimates for another websites traffic. It's not going to be accurate.