IMHO, for what it is worth, some hobbyists can 'get away' with using tap water...even in a reef tank...and it would be relatively easy to see if your tap water is going to be sufficient or if it would be better to go with RO water by testing your tap water with the same tests as you would for your tank when and if it is up and running....including, but not limited to ammonia (before and after treating with a dechlor conditioner since, if present and once treated, chloramines would leave ammonia behind), nitrite, nitrate, pH (high range and/or low range), Kh, Gh, phosphates, iron (both free and non-free), copper (ditto with iron), etc...etc...etc... This will give you the best idea as to how well you will be able to maintain the more specific water chemistry saltwater fish require to thrive.
Don't get me wrong though, I agree with everyone in that RO water will make your life so much easier, even in a FOWLR tank because, as already pointed out, it will help considerably with algae control (although, in a new tank, don't be surprised to see algae coming out of your ears...this would be rather normal in many cases). I do use RO water exclusively myself, but do know at least a few people who do not.