Very important or not important at all, depending on who you ask:
Serious fly tiers would say they are essential. Evidence suggests size and general outline are important when fish are feeding heavilly on a particular forage item and the antena on a shrimp is a fairly conspicuous feature.
If you ask the fish the same question you might get a different answer. The one thing you can be sure of is that their answer will be honest and, generally, their final answer
At the end of the day confidence in the fly at the end of your leader is probably as important as the pattern. I'm not big on close copy immitations - although I do use jungle cock on some patterns
Well, to me it looks better in the water than any plastic stick-on thing ever did and that gives me confiidence. Having said all that, most of the fish I've caught this season have taken flies with no eyes at all.
My first choice would always be something that really looks alive in the water and approximates the size and general outline of whatever I think might be available - or see fish eating.