Is it possible to use AdSense on a free .wordpress.com blog? I can't see any way of doing this in the configuration.
There are options to add text widgets etc, but nothing for adds?
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You can do it If you pay for premium features. With this, your blog will get Ad-control option .Later you do need to contact the Wordpress team using the contact form on this page Ad control.
My advice is to don't expect to earn much from Adsense unless you have 1000 hits per day and are blogging about a subject where the typical visitor is inclined to click on ads. Other wise it would be a waste of your money to purchase the premium package .
Hope this answers your question :)
As for any wordpress.com related question, please pose that question to their technical support as well to get an answer.