That will work but don't assume that everything will be finished quickly. I just ran my new filter side by side with another filter in one of my tanks. When it had been there a month, I moved it to a new tank and put 3 juvenile mollies and 2 swords into the tank. The ammonia was well controlled but I did a 90% water change daily for 4 days before the nitrites stabilized. Today I got my first sky blue nitrite test. Yesterday I found it at 0.5 ppm which it had been for each of 4 days before that.
Lesson to me, you will pick up the right bacteria from an existing tank to start the new filter but even after a month of side by side running, it took a few days to get completely up to where it could deal with a small fish load. I usually clone my filters by cleaning a filter in a new tank and then treating the new filter with a fishless cycle. The clones become established and fully functional quickly so I am starting to think that is a better approach after this last fiasco.