Miller integrator dc offset ->why no gradual increase towards saturation?
Your circuit will integrate the offset voltage in the same way as any other input signal and do what you expect.

You will need to setup your simulation to include the startup otherwise it will delay until the system operating point is stable before starting the simulation.

There is probably a configuration of Multisim to do that.

One way to sidestep this is to put a switch across the capacitor that is opened at a specified time into the simulation (for example 1 millisecond).