I'm building a website that contains certain forms protected by reCAPTCHA v2.
Can Googlebot crawl content protected by its own reCAPTCHA v2?
No it can't.
The whole purpose of reCAPTCHA is to verify that the connection is being controlled by a human and not a machine. If there is content behind the reCAPTCHA protected form that you want Google to index then you need to identify another way for Google to be able to look at it (like giving Google authentication information to bypass the CAPTCHA) but by and large this would be pointless as any page that is protected by a CAPTCHA shouldn't be accessed by a machine and should only be accessed by a human.