Dealing with those captcha controls is tricky business. I would avoid having a hidden one if possible, maybe try adding one dynamcially when you need it instead. You may have better luck not using the mp:CapthcaControl which is a provider model wrapping the different captchas and instead use a specific captcha control like SubkismetCapthca instead. I have fought many battles with the captchas in features where they are used.
Hope it helps,
Joe