I guess that's the theory (though I'm not clear if is this accepted practice or your own reasoning; if you're an economics genius, please accept my apologies- it doesn't matter which ;)).
I'm no genius, and I not sure what group I would be speaking for if I said it was "accepted," but I have studied economics and I work with these issues as part of my job at a large insurance company. I do a lot of basic financial modeling, and work with the people in the investment and hedging areas that do the more advanced stuff. Regardless, you shouldn't take arguments like this at face value from anyone (especially on the internets), and I'd be glad to explain the reasoning behind my conclusion.
There's a couple different ways to define inflation, which does make this a bit (as you say) complicated. As a financial professional, I tend to think of the exchange rates as representing the relative prices of two currencies, and inflation of one currency as a decrease in that price, because that's the most consistent and tractable way to model uncertain future inflation and exchange rates. You're absolutely right that the presence of a free global market with minimal trade barriers (artificial or otherwise) is required for this to match the "cost-of-living" interpretation of inflation. If you measure inflation as the cost of goods for which there is such a market, such as widely-traded commodities like gold, then what I said should hold. If you define inflation as a CPI on an arbitrary basket of goods, some of which don't have such a market, well... that's what I meant about "not actually measuring inflation." Not in a consistent and useful way.
If I'd done the conversion a few months ago, when the Pound Sterling was hovering around the US $2 mark, you'd have got a higher figure than if I'd done the same thing today.
Not if you measure inflation based only on internationally traded commodities. If the Pound has lost value relative to the Dollar since then, then either it cannot buy as many commodities (inflation), or the Dollar can buy more (deflation), or both. Either way, it shouldn't matter what date you choose for the currency conversion, because the proper inflation adjustment will get you to the same place.
This is a bit confusing for people who are used to thinking of inflation only in terms of an arbitrary consumer price index. You might think that if you are making the same number of Pounds, and it buys the same number of CDs, what inflation has occurred? If your CPI basket consisted entirely of CDs, then indeed it would show 0% inflation. However, that's misleading, because you presumably spend money on many things which are ultimately driven by commodity prices and international free trade. Even if you don't, the suppliers of the CDs probably do, which means that even though you're still paying them the same for the CDs, they are feeling the true difference in price.
In other words, despite the stable salary and CD prices, I would say that the Pound really was worth more (relative to the Dollar) a few months ago, so your £X,000 salary and £X cost of CD were both "more" than they are now, even if the only thing you actually bought with your salary was CDs. You were still paying the opportunity cost by choosing CDs over whatever alternatives you had for that salary. Since then, you've received a pay cut (by being paid the same number of a less valuable currency), and certain goods (CDs) but not others (commodities) have also been discounted in the same way. If you still buy only CDs, you'll get the same number of them, but you won't be paying as large of an opportunity cost to do so, since your salary couldn't have bought you as many other goods. (Alternatively, or perhaps additionally, I've received a raise, but many goods like CDs have correspondingly gone up in price.)
This implicit price change can only happen if there are significant barriers to free international trade of the good in question, because otherwise someone could buy up CDs in one country, sell them in another, and convert the currency back to the original at a profit. In fact, this mechanism is exactly what makes the commodity prices a consistent measure. If the exchanges rates of the currencies didn't match up with their inflation (the amount of commodities they could buy), then people would do this trade until the values lined up again. That's how I can be so confident in the practical application of theory, as long as "inflation" is defined that way.
If you try to have a definition of inflation that relates your salary to your consumer prices of specific goods, then if any goods have higher barriers than others, you can simultaneously have "inflation" relative to some goods but not others. I find that to be a pretty useless way to think of value and inflation.