Very much so, to my tastes anyway.
But more important than the variety of beans is the brew method. Primarily pour over for me, with water just off the boil - about 200F. Also I only buy whole bean and grind myself.
Auto drip typically over extracts and makes the coffee bitter (think Starbucks). Percolators make nice coffee but the cleanup is tedious. Moka pots are nice too, I use one on occasion.
And never store any coffee in the fridge or freezer, which is what my mother always did. Condensation will form on the beans and leach out flavor compounds.
Over extraction is what you get when you use less coffee than required. Think, "I don't want my coffee that strong, so I use less".
It has nothing to do with the method. Percolators are probably the worst since they recycle the water over and over the grounds until you pull it off the fire - talk about over extraction.
The flavor and color come from two things, the type of bean and the roast. Darker the roast, the more the sugars are brought out - carmelization, and caffenie is removed.
Both where the bean is from (type) and quality are very important to the flavor profile.
Next up, the water. All the crap in the water is going into your cup of coffee, the filter is not fine enough to remove chemials that might spoil the tastes (think well water)
French press is a great way to make coffee, but use the proper grind. The finer the grind, the more surface area which means more flavor from your bean, but the fine grind is gong to escape the filter press in the french press.