There is no option in FormsCentral for such a distribution of forms and collection of responses.
Not sure how you reach your audience, and it would be work on your part, but you could do something like this:
A different approach would be one that came from a department in the state capital in the state I live in. They wanted to collect hundreds of responses, and asked respondents to essentially create their own unique identifier, using the following formula:
This method gave them some assurance of the anonymity of the responses.
Hopefully you can come up with something that works for you,