Could require solving a captcha to submit anonymous questions?

Since we already got quite some spam it’d be nice to block this with a captcha if one submits a question anonymously.

No - captcha won’t help, as the spammers are not anonymous, they register using an email address/openID just like everyone else. So adding a captcha will not help.
(furthermore the spammers didn’t bother to check “ask anonymously”, but used their nick)

Right, and it doesn’t seem the current SPAM is automated, which is the primary reason to use CAPTCHAs.