Aight so, as promised, I'm testing this out now. I decided my test subjects would be none other than the event Pichus-- Spikey Eared Pichu and Pikachu Coloured Pichu. Before I put them into the daycare, Shiny Pichu has 205 Happiness, holding the Soothe Bell, and Spikey Eared Pichu has 72 Happiness. The true test begins.
I plop them into the daycare, get my bike ready, and set a timer for 10 minutes.
10 minutes later, they both grown two levels. This should be enough to check.
In the app, it says Shiny Pichu has happiness of 205, and Spikey Pichu has happiness of 72. Nothing has changed, even for the Pichu with the Soothe Bell.
I hope my experiment answers your question-- the soothe bell does not raise happiness in the daycare.