I'd say that while it's not "overly" important to have a coach actively competing, themselves, if you're just starting... but they must be actively taking clinics and lessons themselves.
Eventing is a sport where if you try to "flub" your way through someone will get hurt... one of my biggest pet peeves is coaches who are coaching beyond their scope, well past their own ability. It's recipe for disaster.
The other thing is, it does you no service to learn "wrong" then have to "fix" bad habits that weren't caught earlier as you get better. Best to just start with a coach with some solid achievements behind them... they need not be olympic medalists, but they should at least be competent and active in what they are teaching.