Yes it is possible and there is more than one way to do it, but the first step is to set up an email service that supports such emails. Many ISPs limit how many emails you can send out in a given time interval and this will keep FileMaker from being able to do what you want here. There are SMTP servers you can find on the web that support this type of email volume.
As for FileMaker. What are you able to do now with it? What's your starting level of expertise? Can you use the Send Mail tool to send a single Email from FileMaker? Do you know how to create scripts? Do you know how to create calculations?
With Send Mail--usually set up with a script, you can construct a calculation that puts a plain text email in the body of the email that can combine "boiler plate" text with text from a specific record in your database. You can even set up a "template" table where each record represents a different set of "boiler plate" with placeholders for data from different fields in your database. Then it's just a matter of selecting the correct template record and the correct set of recipients for your email and then Filemaker does the rest in a script with calculations.
There are services on the internet that send, monitor and track fancy personalized emails.
Constant Contact is probably the best known.
I prefere Madmimi and MailChimp - both allow free accounts and good howto videos.
This site has a good description of the options and details