Hey there seems to be some confusion about this. Actually, when we talk of offset of a MOS Operational amplifiers, the measurement is about the systematic and random offsets. So, the total offset is the sum of these things. Most importantly, when we design the amplifier, we measure o/p voltage for VDD/2 input on both terminals. So, the offset voltage is the (voltage seen at the output - VDD/2). this is the systematic offset.
Random offsets come from process variations. Good layout techniques will help us to evade that.
Coming back to the question, your opamp can never have a 1mV input referred offset voltage for a gain higher than 30 dB. It is enough to saturate the outputs