Nope, doesn't work that way. If you buy BTC with fiat and you end up mining less BTC than the BTC you spent on the hardware, regardless of what fiat you paid, you've netted a loss. The conversion from fiat to BTC doesn't matter, because you paid in BTC. Let's do some math (complicated tax issues out of the picture).
We're going to simplify the numbers, so it's easy to digest:
Scenario A: You purchase 1BTC for the exchange price of $100USD, then immediately purchase a miner that costs 1BTC. It's super-fast! During the lifetime of the device (which we'll say is the time that it makes more in BTC than it costs to feed it electricity) it produces 0.93BTC before you're mining at a loss. When you go to the exchange, BTC has doubled in price to $200USD. You exchange your 0.93BTC for $186USD. This appears to be making a profit, until you get to...
Scenario B: You purchase 1BTC for the exchange price of $100USD, then hodl it. When you go to the exchange (at the same time as you would in the first scenario) BTC has doubled in price to $200USD. You exchange your 1BTC for $200USD. You did no mining, and doubled your money.
In the first scenario, you lost BTC, period. Regardless of what the fiat rate is, you will always get less exchanged fiat if your miner cost more than it made versus just holding the BTC. There's no getting around that, you lost BTC. Profitability in mining should always be calculated in BTC if you paid for the gear in BTC.
Now, the inverse is true if you paid in fiat, and I know that sounds crazy! If you buy a $100 dollar miner in fiat, and it generates BTC that you later sell for more than $100 dollars, you've made a profit. It works this way because the "value" of the dollar is (mostly) fixed, where as the value of BTC is not. If you pay in BTC, you need to make your profit estimates on BTC. If you paid in fiat, you should be using fiat to base your profit estimates.
That said, I enjoy mining and I've been lucky enough to turn a profit (in BTC!) on my mining endeavors so far--this isn't me shooting down mining by any means, I just know the math is confusing and want to lend a hand. I myself had to sit in a recliner and sip scotch while I worked it out! Everyone should give it a go, as it's an excellent mental exercise.