I just use captcha buster extension in Firefox, captchas are just stupid and it makes more problems for humans than for robots.
AOSP from my knowledge uses some google addresses like DNS, time server and connectivity check google servers but unless you will install GMS (Play Services), no private data will be sent to google by default.
I just use captcha buster extension in Firefox, captchas are just stupid and it makes more problems for humans than for robots.