It won't factor in songs when making the discover weekly that were listened to in private mode, however the daily ones it doesn't matter for.
It's also a bit annoying to have to everytime I go to the gym not only have to find what I want to listen to, but also remember to go into the settings, scroll down, and turn it on, and make sure to turn it off in case I don't want it to stay private for the next 6 hours.
I wish it turned on based on location. Hell even if there was some intent or way I could trigger that to turn on/off from Tasker I could automate it myself :P.
I'm really bad at finding new music or just music to enjoy in general that I'd like and it's a huge annoyance to have shitty suggestions. Lately I don't even use Spotify much and have been considering just cancelling it.