Actually you can!
And it’s dead easy and very impressive
You need to make your fish as a set of splines and Loft a skin over them.
Now draw your fishy path and make each of the splines follow the spline as tangent. You need to make each fish spline lock onto the path behind the one in front at the right spacing. (That’s where I get a little misty)
I have just looked at my file – you need to copy the same number of path spline on top of each other as there are segments on your fish. When you animate each section is set at a different ‘start’ percentage along their individual paths. (I’m sure you can do this on one spline??)
Now as you animate, the fishy splines move together along the path and give a perfect fishy movement and the loft is a really good skin!