reCAPTCHA does not support Opera Mini (or any other Presto engine based browser) as well so this likely won't be a solution. At least - not ultimate.
This approach might be used as a workaround for some extent as the website might see different request source IP (at least if website is not prepared to handle "X-Forwarded-For" HTTP header containing true source IP address) and may pass user on without requiring to solve the reCAPTCHA.
On the other hand Opera Mini IPs are shared by many clients so they might look suspicious as well.

The other idea that came to my mind was to create an extension or some JavaScript user script or bookmarklet to use a captcha solver service to bypass it.