Using "pure" water in a brackish tank, as opposed to that from the municipal supply, is probably pointless. As you probably realise, the extra hardness in tap (faucet) water is a good thing in a brackish tank, where a high and steady pH is desirable.
As far as combating algae go, it won't make any difference. Large brackish water fish like scats, monos, and puffers will be pumping out so much nitrate and phosphate that the 10 or 20 mg/l in the tap water supply will be neither here nor there. In tanks with smaller, low-salinity species, like gobies or orange chromides, you'd do much better using salt-tolerant plants (of which there are many) and using those to stop algae. Plants are far and away the best method for combating algae.
If you happen to have a surfeit of pure water, then try keeping a soft water aquarium. Very challenging, but worthwhile.
Cheers,
Neale