No, the Testnet is only for testing only you do not earn any Bitcoin Gold, you will have to wait for the Mainnet to come online. I'm using the Testnet to check out miners, just started with Claymore for now, to see what sort or return I would expect to get.

EDIT:
You can do test mining at http://btcg.miningspeed.com/ to see what sort of hashrate and BTG returns you'll get.
BTG Calculator, https://www.crypto-coinz.net/crypto-calculator/