Yes & no. Green tea with caffeine is a category c drug that is probably ok in moderation early in pregnancy but worrisome as you approach term. The newborns system cannot metabolize it easily (1 wk to eliminate 1/2) & they can get jittery, fussy. Pregnancy is a time to consider anything you eat/drink for the health promotion value. There are decaf green teas out there.
No. Green tea has caffeine in it so should be avoided, just like coffee and caffeinated sodas. Try switching to herbal teas or find a green tea that specifically says it is decaffeinated.