A few minutes later I came up with an idea.
My test results lead me to believe that clip effects apply before track effects.
Opened a multitrack session, generated a 100Hz base frequency Square Wave at 30% cycle. My idea was that I needed to use two different in-built plugins that would generate two visibly different outcomes and which each had a visible input waveform monitor. For convenience sake, I used Multiband Compressor (on Broadcast preset) and FFT filter (with a nearly-square band-cut between 100Hz and 1kHz) as these are the plug-ins I'm most familiar with.
I added one copy of each effect to the clip effects rack and track effects rack, but toggled their enables in such a way that the FFT Filter on Clip Rack was enabled, alongside the MB Compressor on Track Rack. The result was that when playing back, the MB Compressor on Track Rack received an input waveform with a large notch cut out between 100 and 1000 Hz, but toggling the MB Compressor did nothing to the height (amplitude) of the input waveform for the FFT on Clip Rack.
I then reversed the enable toggles. This time, Clip Rack had the MB Compressor on broadcast preset enabled, and the Track Rack had the FFT enabled. During playback, toggling the FFT on Track did nothing to the Compressor on Clip's input waveform, but toggling the Compressor on Clip Rack changed the height of the input waveform on the Track Rack.