If I understand you question correctly.. the answer is yes. That is the general process for making KT. Boil 4 qts of distilled or reverse osmosis water.. add 2 green tea and 2 black tea bags.. steep for 10 minutes.. pull bags.. add 1 cup sugar and stir until dissolved and let cool to room temperature.
Hopefully, you have acquired a cup of kombucha tonic/tea to add to the sweet tea you have made. Add it and then add the scoby.. cover with a tight woven cloth (t shirt piece) with a rubber band and store in a room temp dark place for a week or more depending on your taste.
If you don't have the cup of tea from the person you received the scoby from, you can add a cup of raw apple cider vinegar.. but, it's best to have KT. I also understand you can buy a raw KT from a health food store.. or, if you have a Whole Food store or possibly a chinese market.. you might be lucky that way. I've found GT Dave's Kombucha (original, unflavored, raw) to work as a starter just fine.. It's expensive.. but, for a one shot deal.. not bad.
Hope this helps.
Oh, re your original question.. Yep, I think you will likely be ok with just the scoby.. but, the acid in the KT will help prevent mold from forming, giving it a good head start.
Also, don't add too much sugar.. you need to find a balance so you don't overpopulate with yeast.. 1 cup per gallon seems to work.. you'll find your sweet spot..
