I could see this working, although the one week seems a bit optimistic considering it will take a few days campaigning or clicking faucets to come up with the initial investment. Also, it would be a great way for newbies to learn about trading, only risking the little bit of time/effort they spent at faucets or posting on the forums here, which they were at anyways simply by reading this.
But back to the topic at hand, say that original investment of 500,000 satoshis was spread amongst say 5 different investments, for sake of simplicity lets say each was trading at 50 sat when purchased. We would have investments A, B, C, D, and E each with 2000 of their respective coins as the beginning balance and a starting value of 100,000 sat each. Then after say 3-4 days we have the following results:
Coin A: 30 sat * 2000 = 60,000 sat (
loss of 40,000 sat)
Coin B: 10 sat * 2000 = 20,000 sat (
loss of 80,000 sat)
Coin C 160 sat * 2000 = 320,000 sat (
gain of 220,000 sat)
Coin D 60 sat * 2000 = 120,000 sat (
gain of 20,000 sat)
Coin E 20 sat * 2000 = 40,000 sat (
loss of 60,000 sat)
So we ended up gaining 240,000 satoshis and losing 180,000 satoshis, which would be a net profit of 60,000 satoshis, or a little better than 10% gain of the original investment. We lost 3 out of 5 trades, but since they probably won't go to 0, they don't necessarily sink the entire investment into the ground. Also, one could try holding the losers for longer, but for this example we would assume everything gets cashed out and the end of the cycle with everything reinvested anew. Of course it is pure speculation, and luck will play some role, but it is not out of the question by repeating this method over a longer period, perhaps a month one could earn 1 BTC.
I think the big drawback to this is it is limited to how big of gains you can make. The next month you simply can't pluck sown 1 BTC into a coin that was averaging only a .1 BTC daily volume and expect others to buy it up. You would need to spread the coin around quite a bit and after a point you will run out of candidate coins to invest in. So going from 1 BTC, to 2, 4, 8, 16, etc and expecting to be a millionaire will be highly improbable, but I could see someone starting out and playing around a bit could earn 1 BTC a month doing this. Of course, as others catch on this will also cut into the profits somewhat.