Will my participants ever receive spam or unwanted text messages after they vote?

Never!

The responses are private and the phone numbers that your audience is voting from will not be transferred to anyone under any circumstance. The main reason we keep track of phone numbers is to identify the caller ID so that we can limit votes per polls as needed. That is the sole reason we capture phone numbers / Caller IDs. Your privacy and the privacy of your audience is of the utmost importance to us.