it shouldn't be a problem to define custom stock group with ASX stocks - there are ASX stocks in our SQ Data service.
You don't need to define the time anywhere, stockpicker trades on daily timeframe.
So generating/testing strategies on ASX or your other stocks imported manually shouldn't be a problem.
The question is how you'll trade it. We are developing ou own cloud trading platform to trade this kind of strategies, but we'll support only US exchanges initially.