As usual, I guess arrangement is 75% of mixing. I imagine opera composers do a similar thing, thin the arrangement out during the singing and crank it back up in between. 

Would it be silly to use side-chaining for this?

It depends on what you want to side chain. If you mean the whole orchestra, yes but then it could sound like it. i.e. every time an effect comes along the orchestra ducks. And then comes back in when the effects os gone.
 
You could side chain a few things in the orchestra though and leave the rest alone. The idea is to leave part of the orchestra at normal volume while the effects are present. The non distracting parts or parts that are not in the way of the effects.  The idea is to look at the tracks that may be distracting at the exact time of the effects and either drop those parts out all together or down. Often it is only a few things that are getting in the way and not allowing effects to be clearly heard.
 
Less is more. This whole process in a way is leading up to good arrangements. Not having unnecessary parts present.  You have to be not so emotionally involved with the parts. Be able to let things go that are cluttering things up. 
 
Let the effects for those seconds be the melody in the music. Think of it that way.

Sounds like a perfect job for Melda Production MSpectralDynamics.  Put MSpectralDymanics on a group track of the full mix of the orchestra and use the effect sound as the sidechain.

jamesg1213
As soon as I read the thread title, Scott Bradley's brilliant music for the Tom & Jerry cartoons came to mind.
 

Terrific video. Everyone except one trumpet player in the back near the end seemed to be having a blast. Thanks for sharing!

jamesg1213
As soon as I read the thread title, Scott Bradley's brilliant music for the Tom & Jerry cartoons came to mind.
 

 
Now THAT was fun!!  especially so for me being a trumpeter/trombonist, GREAT orchestra!

That clip was excellent and a great example of the music for a later effects thing or even as it is there are plenty of effects in it now. 
 
I did want to mention something which I have not. Effects generally fall into two types. One shot e.g. foley for a short time duration, or any time that is greater than a one shot the effects become  atmospheric or atmos for short.   One shot effects are great and if in say an animation someone landed on the ground hard and a short sharp powerful percussion sound was constructed by the effects guys then all of the music can actually stay in.  It would enhance any melodies going on at the time. Punctuating rhythms in the melodies.
 
What you do have to be mindful about is all the tempo modification you need to do around those hit points so the effects land on or sub divisions of beats. But that is more about scoring music and effects to picture.
 
Atmos effects do last longer and much longer often so clearing away some parts even around the start of an atoms effect will help to clarify it a bit. Things can come back in towards the end of an atoms effect thereby smearing the areas where effects end and music continues on.  These were the effects I was referring to before.