I have read that it can be done as you say WD but my own experience with trying to use a filter that was not seeded but just ran side by side for a month was that it was not properly cycled and I had to seed it with a filter cleaning to establish the bacteria in it. I did just that side by side for a month and placed 2 juvenile swordtails into the supposed cycled tank. When I got a large nitrite rise, I washed a filter in their tank and let that seed my sort of new filter. 3 days later the emergency 90% daily water changes could finally stop because nitrites had settled down. I have no doubt that the ammonia in a tank will keep a cycled filter ticking over but a few weeks side by side was not enough in my case.
It more or less acted like a filter that had been in a fish-in cycle for a month but the other filter had been keeping the tank safe for the occupants. It left me with a filter in the middle of the nitrite spike.
Running a new filter side-by-side with a current filter in a cycled tank is not really going to speed up the colonization of autotrophic bacteria in the new filter, maybe a bit. Since the autotrophic bacteria do not live in the water column, this means that they cannot simply get up and march out of one filter and into a new one.
Instead, running a new filter side-by-side with a current cycled filter is going to allow the new filter to become cycled,
without adding any ammonia (fishless cycling procedure) to the tank, or doing daily water changes (fish-in cycling procedure).
So, by running a new filter in a cycled tank, is going to allow that new filter to become cycled without you, the owner of the tank, doing really anything but keep on maintaining your current tank the way you did all along before adding the new filter.
1 month is more or less a guideline of time that, on average, this process may take place; the colonization of Abac's and Nbac's within the new filter in an already cycled tank.
So, in conclusion, this is more like a "stress-free" and less time consuming procedure to colonize bacteria in a new filter, without doing any fishless or fish-in cycling or adding mature filter media to a new filter.
OM47, I know you know this, so I am not ripping on you...lol...

... just thought it might be helpful to the OP.
-FHM