No. Even if you use Firefox without login to google account on it, you usually only face few more captcha.
Yes, Google reCAPTCHA is known to be hostile against Tor users. Even worse, after you done solve all captcha sometimes, google might refuse to let you pass with this message "We're sorry, but your computer or network may be sending automated queries. To protect our users, we can't process your request right now.".
Use paid VPN and connect to server on unpopular country. After that, get URL which can bypass captcha.