Absolutely. There is an opt-out option on your Member Dashboard, directly under your balance of available and redeemed balloons.
If you opt out of the Balloon program, your Dashboard will no longer show Balloon information and if you hold a Balloon, this will not show on your Profile page.
You can opt back into the program at any time by going to your "Account Details" page and checking the box ‘Accept Balloon Exchanges. Once you opt back in, any Balloons that you had will still be there.