The best thing IMO is to use Audyssey normally, but still use the Umik-1 for things like:
1. Measure the need and effect of acoustic treatment (complicated, but does require a mic to even get an idea what's going on).
2. Optimize speaker and subwoofer positioning pre-calibration based on REW measurements (which positions measure best).
2.a. In case of multiple subwoofers, you can even just measure a single subwoofer in each position, and then use REW to calculate how each set of positions would sum up, to pick the optimal set of positions from within the possible positions which you measured.
3. Get an idea what Audyssey actually did and what it can/can't deal with.
4. Verify levels with REW-generated pink noise with Audyssey enabled (use REW as a noise generator and as an SPL meter, no need for separate meter if you have a Umik-1).
5. Measure speaker+subwoofer integration (measure each channel with crossover and audyssey enabled) and optimize by adjusting the subwoofer distance if needed. Audyssey measured distance doesn't always provide optimal results, and for me 1 of the front speakers actually got very bad results with Audyssey measured distance.
So yes, even if you don't use the microphone to generate calibration filters, there are still very good uses for a Umik-1 and REW. Generating filters is also really unnecessary if you have automatic calibration system like Audyssey or Dirac, plus you don't really have where to insert those generated filters anyway unless you use the trick with MultEQ-X which basically disables the automatic calibration in the process, and while it works, nobody have proven that it provides any improvement.