Given how much the game has changed since patch 2.0 introduced the achievements, the question of achiements and mods becomes less clear than if the game had been changed very little since then. For example, I got the S.P.Q.R. achievement shortly after SoA, which most likely would have become easier with 2.1 (due to factions being easier to defeat; though I would have been less able to grab land from rebelling vassals), harder with 2.2 (due to the vassal limit, and possibly other things), probably unaffected by 2.3 (though playing with WoL might lead to crazy focus stuff), not overly affected by 2.4 (though HL could have made a large difference), and much harder with 2.5 (due to the ERE starting out large enough that there *will* be Defensive Pacts forming if you try to expand even half as rapidly as you could do in 2.0). It is still possible to roll back to a different patch to grab that achivement (and a lot of others) if you don't want to try getting them with the current version, but that's in many ways similar to modding the game (though somewhat more official), so in a way the argument that the unmodded game is the way the game is meant to be played falls apart due to that.
Some of the most basic achievements (get married, play until the end, become a duke in one generation, etc.) would, in my opinion, make sense to open up to mods and perhaps even non-Ironman games. Others (e.g. become king of England as Denmark in 1066) could easily be cheated with mods by simply giving your character lots of troops/money/prestige/etc., which can make a difficult achievement very easy. Then again, as achievements have no effect and mostly are a way to keep track of the fact that you have managed to do some things, letting people get them even with mods wouldn't give people an unfair advantage, though those who had gotten the achievements without any mods might feel cheated as they had to spend time and effort to unlock something that became trivial with mods.
