Matt, that's not how that works, I'm afraid..
Although both boxes say 1GB required (in your case, as I make out..thus xp, right?) you don't add those on top of each other, the specs on the NH box, are just the SS08 specs..
But your RAM is WAY below specs, mate. 248 is not a lot..
You need 1GB to run the game (+NH) on XP, and 2GB for vista. Though it's wise to have much more of course, cause being on the low end, it will mean you can't make it go at full throttle, so to speak.
But adding NH does not double the needed RAM.., though NH might run a tad bit 'heavier' and being close to the minimum specs can mean that performance after NH installation might be a little less good.
Regards,
Fred