Nope. Living in Europe, playing on Canadian Servers, never had problems.
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If you're playing on a Japanese server, you shouldn't be suffering from latency so extreme that you cannot (eventually) clear all available content. From what I understand, AU<->JP latency should be similar to Germany<->Montreal latency. Battleping does in fact have servers across Asia, including in Japan and Singapore.
We have an Australian player who uses Battleping to play on an NA server. This player has been with us since the launch of 2.0 and not only passes latency-induced gameplay checks, but also excels. We also have a player living in Japan and many Europeans.
That being said, you may encounter your fair share of "no fucking way" moments, which can be incredibly frustrating.