You would come extremely close IMO. Unlike BTC ASICs in which increased hashrate correlates with decreasing hardware costs, the cost/hashrate of Eth has very little impact on the price of new mining hardware. This is what 11c/kWh and 20MH/s looks like assuming you start mining now and continue for 3 months if the hashrate doubles monthly.At today's price ($10 per ETH) and difficulty a 380 will earn around $90 a month, after power costs. But the difficulty level has doubled in the last month and seems set to keep rising rapidly, so I'm not sure you'd ever recoup the cost of the card.
I bought my last mining card about three weeks ago, and won't be getting any more. I can't see a scenario, short of a massive jump in the price of eth (not impossible, of course), where it would pay off to buy new cards now.
You end up making $96 after power costs, which wouldn't pay off the card but would subsidize more than half its cost.
Baring an Eth ASIC coming out though, this is an extremely unlikely scenario. If you go back to the GPU mining days with BTC, you would find that with a stable price the network stabilized at the point where reasonably low power areas had a reasonable payoff period. My gut is saying that it was about 8c/kWh and 180 day payoff, but it's obviously been many years now and I don't feel like looking it up.
It's relatively reasonable to look at the graph there, and say look at the day 50 point. There you're making about $1.1 gross per day. Let's say your all in cost to add a ~20MH/s 380 is $220, which is the card and a portion of the PSU, MB, etc. That's a low ball, since without MIR the cost of a 380 is about $190, but whatever. At that point, even for someone with free power you're looking at a 200 day payback, and the possibility that earlier than that the network might switch to PoS.
I would imagine (at the current 10-11 price) that we might see the network double again over the next two months, and then maybe gain another 50% over the following 2 months. Even if you go with doubling in 2 months and doubling again in the following 2 months, you'll end up with at around the $180 mark at the start of August. Depending on when you think Polaris will launch (back to school season?) that's about right to fulfill your requirement.
Again, all IMO. YMMV, etc, etc.