If donors send donations via PayPal, can their email addresses be automatically captured into a nonprofit’s database?

You can do this with something called the Instant Payment Notification (which is free, you just have to turn it on). See https://www.paypal.com/ipn for more information.

There are several companies that provide scripts to add to database:

• PayPal IPN Plug-in Script: http://bakery.cakephp.org/articl...
• Code Examples for IPN as provided by PayPal (you need to understand programming for this): https://www.paypal.com/us/cgi-bi...
• Donations Tracker (includes database addition): http://www.stellarwebsolutions.c...
• WordPress PayPal Donations Plugin with IPN + Database: http://wordpress.org/extend/plug...
• Same plugin as above - official site: http://www.nonprofitcms.org/2010...
• PayPal IPN Listener - https://cms.paypal.com/us/cgi-bi...
• You can try contacting these folks and see if they will allow or code a database option for you - http://www.phpjabbers.com/paypal...
• Here is another script - it will push the buyer's information into the database - http://www.micahcarrick.com/php-... - you can have a coder write a script so that it can query the DB and export the list out as a CSV file or a text file. Do look at this page for the flow diagram of how the IPN works: http://www.micahcarrick.com/payp...

Essentially any decent coder ought to be able to help you work with your IPN and put the Buyer's information in a database for you to work on.