Yes, it's perfectly possible, but not very likely.

It can happen through direct resonances, as in $p \overline p \to J/\psi \to e^+e^-$, or through virtual particles, as in $p \overline p \to \gamma^* \to e^+e^-$.

(Timescales for the intermediate state are much shorter than microseconds.)

It doesn't happen very often because the proton and antiproton can annihilate through the strong interaction, so reactions like the second are scarce compared to annihilation to pions. Also because at high energies the proton should be thought of as 3 quarks, and a reaction like the first involves all six of them co-operating, so is scarce compared to processes where only one quark pair annihilates and the other 4 are merely 'spectators'.

Yes, it's perfectly possible, but extremely unlikely.

It can happen through direct resonances, as in $p \overline p \to J/\psi \to e^+e^-$, or through virtual particles, as in $p \overline p \to \gamma^* \to e^+e^-$.

(Timescales for the intermediate state are much shorter than microseconds.)

It doesn't happen very often because the proton and antiproton can annihilate through the strong interaction, so reactions like the second are scarce compared to annihilation to pions. Also because at high energies the proton should be thought of as 3 quarks, and a reaction like the first involves all six of them co-operating, so is scarce compared to processes where only one quark pair annihilates and the other 4 are merely 'spectators'.