Nah.
Green tea has some good health benefits, including a lot of antioxidant factors, but raising your metabolism enough to "automate" weight loss is not one of them.
The people who claim this say that the caffeine in green tea raises your metabolism enough to make a significant difference in how much weight you lose. The truth is that in order to raise your metabolism enough to make a SIGNIFICANT difference, you'd have to consume enough caffeine to be the equivalent of drinking 40+ cups of coffee a day - and if you're getting that much caffeine from a green tea capsule, I suspect you'll have other health issues first!
Caffeine does have a SMALL thermogenesis effect - that is it raises the temperature of your body while it is processed, but not nearly enough to make a huge difference.
The biggest aid to weight loss provided by any tea, including green tea, is that caffeine acts as an appetite suppressant for a lot of people. This is why it's included in most diet pills and why drinking a cup of tea or a cup of coffee before meals or to help with a craving often helps people lose weight.
But it's not because of any specific benefit of green tea capsules that you can't get from drinking a cup of tea of just about any kind, anyway.