It would be good for the track that your putting the notes onto to have an effect on the notes that you’re putting in them; so, you’re FX chain could be used to EQ different drums/sections from a sliced loop (so they’re statically set), but then for dynamic effects, things like filter sweeps for specific sections/drums (e.g. the snare slice from a drum loop), you could copy over the notes/snare section you want to sweep/effect to a different track to the main pattern/slice/loop and automate a sweep or any dynamic effect. Either this, or for FX chain automation to work like track automation does. But, both would work, both would make sense.
This is a (sort of) standard feature and seems odd for it to be any other way. It’s similar to routing/sending FX chains to certain tracks, but, in addition to the SEND track plugin you’re automating, or the FX chain plugin you’re automating, you could/should be able to automate (ideally in addition) the track that your note data is playing on. I’m not sure what order it would be in, but, just like in another DAW you can have a track with effects on it, which you send to another track/bus/aux that has effects on it, which you can in turn send to another track/bus/aux which has effects on it, AND, you can send it to multiple tracks/bus/aux at once for frequency splitting, etc.