As in the past, with my experience, as long as the ROM you are using is based off of the same build it will work. In this case, as long as the ROM you are using is based off of 4.0.3 being this is the version of google apps then there should be no reason they would fail to work correctly.
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That is not entirely true tho. Reason being is some of the ROMs already have the Gapps in the ROM being flashed & others you have to flash Gapps separate. So lets say a ROM has the Gapps as part of it, just because the ROM & About screen says 4.0.3 after flashing does NOT mean all the Gapps are going to be 4.0.3, it could be the /system base is 4.0.3 but apps are a mix of 4.0.3 & 4.0.4 stuff as i've seen it first hand myself.
I will say in the majority of cases you are correct but there is times where it is not the case tho. So we all just need to be a careful when flashing different stuff to NOT cause issue. I know what a pain it can be to fastboot back to have to start over. So i try to make an honest effort to make sure we have the full skinny on what is working and what doesn't between all the different ROMs seeing as these devs can crush us with updates on a daily basis almost