In terms of performance attribution, you most certainly can separate the performance of the local currency market and the currency appreciation, which can be useful for diagnostic purposes.
Whether you can invest in that is trickier. In fixed income, you can hedge out currency because (for many kinds of FI securities), you know what payments are due when, and can enter derivatives contracts in the right amounts to neutralize currency effects. However, with equities, this isn’t really possible, because the values fluctuate too much. The best you can do is a “sloppy hedge” where you make some estimate about average equity appreciation rates, hedge that currency amount, and hope you’re not off by too much. Or you find a bank to take on the risk for you, but that’s almost guaranteed to be more expensive than it’s worth, or the bank would never take the other side of the deal (however, if you are far more risk averse than the bank, you might still see a benefit that you couldn’t realize on your own).
The last time I did the research, international equities still provided diversification benefits, particularly emerging markets, but the degree of benefits are lessening over time because of globalization and financial liberalization. It is possible that as countries face increasing political pressure to set up capital controls in a post-crisis world, international markets will become somewhat more segmented and diversification benefits will improve, but thus far we haven’t seen it.
Remember that diversification protects against ideosyncratic or non-systemic risk, so the idea is that a diversified portfolio is more efficient in converting your willingess to take risk into expected returns, because you won’t be paying for risk that is just as likely to outperform as underperform over the long term. It does not mean that you won’t have systemic risk (which is basically the risk of things going bad when everything else is bad too). The only way to neutralize that is to hold a different asset, like cash - which exposes you to different risks.
The other thing about diversification is that low correlation isn’t the only thing that matters. You still have to have a sharpe ratio high enough to make the asset a valuable addition to the portfolio. In a diversification context, that sharpe ratio doesn’t have to be enormously high, but it must 1) be positive, and 2) greater than the sharpe ratio of the original portfolio times the correlation between the portfolio and the asset.
If you are adding an asset with a negative sharpe ratio to a portfolio, you’re either 1) hedging, or 2) being dumb. If you’re hedging, you’re doing that because there is a specific risk that you’ve identified that you don’t want exposure to.