This is a great question, a favorite topic of mine trying to get traditional and online advertising to work together.
I am not sure if you can directly link the press releases (typically a shotgun style release) to the DM campaign. If however, you could identify some relevant keywords that people who received the mailing would be likely to type in, I would definitely include those in the PR text, as well as link back to the site/landing page.
Something else to consider would be Google Adwords- there are advanced options to target ads right down to the zip code level and even time. For example you could schedule Adwords campaigns to start at 5PM for keywords related to the business name in cities you mailed to. Also, you could use retargeting- placing cookies on your website so that visitors who receive the mailings can be targeted with banner ads. There are some other things you could do with PURLS, in mailing QR codes Etc.
Direct Mail Marketing for years.
Now Adwords Certified Expert http://www.searchermag.net/google-adwords-consultant/