Can I rely on a the simulation of an op-amp based differential amplifier without looking at my op-amps common mode signal
I would suggest getting a better model if it doesn't handle input range.
For example, here is a voltage follower LM358 powered from +/-5V with a 10V sine wave applied to the input through 100K:

As you can see, it models the output railing at approximately +4V (typically) and about -5V.
That's LTspice with the National Semi model, this one, I believe. It's still a macromodel, not a transistor level model, but it at least doesn't lie to you on such basic things.