Give It A Shot...
While the Yamaha HTR-5890 is rated at 140Wx 7, I can almost guarantee you the Adcom at 100Wx2 will drive your mains more efficiently and cleanly. This would be fairly simple to verify by connecting some decent RCA cables from the pre-outs of the 5890 to the inputs on the Adcom as you noted, then make sure if there are any trim pots/volume dials on the Adcom that they are turned all the way up. From here, you'll need to pull your L/R main speaker wiring from the 5890 and go directly to the Adcom.
Once you've verified you're getting a signal to both speakers, run the test tones and re-calibrate with an SPL meter or however you typically do, assuming you do. This step will avoid any output level issues you may experience between the Adcom and the Yamaha. If you're only doing this by ear, I suggest you consider buying a Radio Shack SPL meter or using the YPAO, if only for the speaker level settings (distance and subwoofer settings for the YPAO aren't terribly accurate).
After re-calibrating your mains to level match the rest of your speaker configuration, do a test run of a movie or two with some dynamic scenes/chapters that you're fairly familiar with. I'd suggest gradually increasing the level to a volume that is close to or at the maximum you would prefer to listen to. In addition to this, play a couple of CD tracks, again ones you're fairly familiar with (multichannel discs would be a good test as well) in 2 channel mode, gradually ramping up the volume to reference levels or as close as you'd like to come to that to see if you can distinguish any benefit running w/the Adcom.
I decided to experiment with exactly this type of scenario and a former Denon 3803 (110Wx7) receiver coupled with a Harman Kardon PA2000 (100Wx2) a little over a year ago. Listening at light to slightly moderate levels (down to -35db), there wasn't much of a difference. However, from -35db down to reference level (0db), the signal was less strained, no discernible distortion, which I didn't previously notice the Denon straining at these levels and the source became noticeably clearer.
Your results may differ based on your own hearing capabilities, your listening environment and other variables, but I believe you'll be able notice the difference and it should improve the overall quality of the signal for your mains... -TD