If you don't have any other options, I'd go ahead and try it with a few minor adjustments. Keep in mind that recipes like this are really loose and based a lot on personal preference. If you don't think the mangoes are really sweet now, the spices may mask some of that, or the sweetness may dull some of the spice.
The ingredients you use will also greatly affect things, as peppers change spiciness by water content, for example, so at different times of year, this same recipe may turn out barely-noticeable spice or barely-bearable spice! Adjusting to the level of spice or sweetness is one of the complications and will require some testing to get it where you like it.
Try soaking the mango, alone, for two minutes in one cup of water - in your (two cup - assuming you have a standard sized one) measuring cup. Some of the surface sugar may soak off in that time, reducing the total impact. Put the mango in the pot you're going to use for the simmering phase. Now, see how much water is left in the measuring cup.
How much water the mango absorbs (which probably won't be a lot, but may be... I'm not sure) will affect how much water you use for soaking the rest of the ingredients.
If there's less than a cup of water remaining in the measuring cup, add that same amount of fresh water to the rest of your ingredients and let them soak for two minutes and finish the recipe.
If it's only absorbed a tiny amount, add the full cup of fresh water to the rest of the ingredients and let them also soak for two minutes and continue the recipe.
You may also consider omitting the brown sugar. There are many other flavors in the recipe, so the loss of it may not hurt.
When it's done, if you do think that it's too sweet, use an acid to tame the sweetness a bit. In this recipe, something like lime juice (try half a lime) may help without being too different. Mango and lime are pretty nicely complimentary flavors and both common to the region. There are even similar recipes out there that include lime. I haven't tried either of these, just showing that they exist.