I wouldn't... Get a test kit and test your tap water. The only reason someone would need a different source of water is if there is a high amount of ammonia in their tap water. Some people also use different sources if they have an extremely high or low pH. They can adjust to pH anywhere from 6-9... Anything over 9 is a little high and anything under 6 will kill the beneficial bacteria needed to cycle the tank.
Even with a low amount of ammonia in your tap, you could use a conditioner like Seachem Prime. That's what I use and it neutralizes ammonia for 24-48 hours which is enough time for the filter to cycle it out.
Also, the only way to be sure your tank is cycled is to test it, and during a cycle it's best to test re ammonia, nitrites and nitrates daily anyways. The liquid test kits are kind of expensive but they are well worth it and more accurate than the strips. Plus, the liquid test kits give you about 800 tests but the strips only give you like 25 in a box so you save a lot of money in the long run.