My avatar is a bargello in a range of nuetrals (mostly batiks, some prints).. so yes ... it can work.
Average ... I've seen bargello patterns use as few as 7 colors, and the upward limit is well beyond 20. I don't remember how many are in my avatar.
Tips .. plenty
1) Take your time choosing fabics. It's not a race.
2) If you use prints or mottles, make sure that the color change from one area to another is equal to or less than the smallest bargello strip you will cut. For example working with a pattern that uses a .5" (cut size) bargello strip you would want to avoid a print that has 3" white dots spaced 4" from each other on a black background. Ditto for batiks with "washes" of color in large splotches of varying shades. By avoiding these you will be able to maintain uniformity of color.
3) Sorting your fabrics - there are two ways to sort, you may need one or both. By color and by value. Two color bargello's will require you to first sort by color and then by value. My avatar is a single "color" bargello therefore I only sorted by value.
4) Sorting by value ... there are three tools that I use. A red viewer (to view all colors except reds and browns), a blue viewer (to view all colors except blues and greens), and a photograph converted to black and white. I use the color viewers for quick views while I working with the fabrics. Once I think I like a selection I take a photo and convert it to B&W. B&W conversion will help you to determine value - but you must have first sorted by color.
5) Once you've decided label your strips. Keep a small sample of the fabric on your design wall with a lable so there is no question which blue is in which position.
6) SPRAY STARCH. You will be handling these strips a lot through the course of the bargello. Spray starch is going to be your best friend.