It would be quite tedious to go to your browser and click + each time you make a pokecenter visit. For leppas its easy, you note down your leppas at the start of your shunting session and note it again once you're finished. Its easy to do that as you can hotfix the leppa to numbers or functions and it can be seen on top.
There are no visual prompts like that for pokecenter visits. So each time you go to a pokecenter visit, you will have to click on your browser and again click on + to record that pokecenter visit. So that's 3 extra clicks every time you need to heal compared to leppa's 0. Quite tedious imo.
However, I have found a work-around for the above tho, as long as you are using this on Windows. You can alter the size of your browser so that it only shows you the mon you are shunting right now and pin it to the top via the deskpins app. This way, you will reduce the clicks from 3 every time you heal to just 1 every time you heal. That's still an extra click but its manageable I suppose.