Molecular Oxygen in Suzuki Homocoupling
I don't remember a direct palladation of arylboronic acids or their derivatives in any of the couplings. Typically, $\ce{Pd(0)}$ inserts into the $\ce{C-Hal}$ bond of arylhalides and is thus oxidized to $\ce{Pd(II)}$. Ouite often, $\ce{Hal}$ is then displaced with $\ce{OR}$ by the action of a base. Think in $\ce{KOt-Bu}$ often used in the Kumada coupling.

In the homo coupling that you described here, there is - for obvious reasons - no $\ce{Ar-Hal}$ for the oxiative addition step. Without $\ce{O2}$ for the oxidative activation of $\ce{Pd(Ph3P)2}$, the mixture will thus remain inactive.