It shouldn't be too bad, but to put all that time and money into something to potentially ruin it because you didn't have an inexpensive piece of equipment (or you had it but didn't use it) is foolhardy.
A little bit of Potassium Metabisulfite will get rid of the chloramine. I put it in when I am heating my strike and sparge water. I have gone to 1/2 RO and 1/2 tap. My beers seem to taste better. Of course everyone's water is different.
Well the classic answer is RDWHAHB. Which is the correct answer in most cases. In your case it is not. Primarily because since this is your first batch you are missing the 2nd H and the B. So just relax and give it time. As long as your staying sanitary you should have no reason to worry.
Tell the arrogant A-HOLE to take a leap! I just brewed an extract (partial mash) that is very good. Otherwise everything I brew is all grain. The upside to all grain is that you are getting the malt from the source! Also more room to tweak recipes, and cheaper. The money you would save...