Yes it does count as one day as long as you're boarding before midnight.
Btw the seating coaches (IC60403) are coupled to the couchette/sleeper coaches (NJ403). It's the same train but you don't need a reservation for the seats unlike the couchettes and sleepers.
It's up to you now to choose which you prefer…
If you decide on the Nightjet please book early, it is sold out a long time in advance
Just a quick note : the Interrail Rail Planner is not the most accurate planner at all, it is updated once a month. Use bahn.de or each companies' website
Thanks so much for your quick reply!