Yes. Exchanges trading different amounts of fiat for bitcoins (difference in price) are in this scenario valuing *fiat currency* differently, because it can buy more and less bitcoin in different places. The arbitragers are the people enforcing Gresham's law by selling bitcoin at a higher price in Japan then 'driving out' the money they used to buy them with to (say) the US, where they buy more bitcoin than they sold.
This is no different from a merchant who can buy an amphora of wine in Rome a couple thousand years ago for the new debased currency doing that, then taking the wine and selling it in Gaul where they value the debased currency according to its real silver value. He trades it for TWICE as much 'bad' money as he paid for it.
Repeat for as long as the idiots in Rome will take the debased coin at the same rate as real silver, and multiply by a thousand merchants. The net effect is the 'bad' money or debased currency all winds up in Rome while the 'good' money or pure silver all winds up in Gaul.
Now consider Bitcoins here to be the 'wine' from the above example and substitute "regulated and manipulated exchange rates" for "valuing the same money differently in different places" and the above is what's happening.