Of course; you can form an HTML page and send it in the mail, the HTML can contain a FORM whose target is your php page, and thus the buttons would cause POST data values to be submitted to the page. Even simpler, you can maybe just include links of the form:
<a href='http://myserver.com/mypage.php?id=1234&action=y'>Yes</a>
<a href='http://myserver.com/mypage.php?id=1234&action=n'>No</a>
Beware using images in emails; its a common trick by spammers to find out when/if a mail was viewed (your browser/client opens the mail, retrieves the image and the webserver logs the image retrieval thereby knowing your email address is valid and read. Outlook etc protect this by removing picture links until a "download pictures" option is chosen. Not cool for your purposes