I've always have that doubt, if we only choose Domination as the victory type available would that change the AI behavior and strategy for trying to win?
It does now, was not always the case.
The code has specific lines for checking if different victory conditions are enabled. I cannot remember if this pertains only to the player or both AI and player. I would imagine both but am not sure.
IIRC each AI does not look at a Victory Condition until a set number of turns in, I think 50 but cant remember, so you would not see any behavioural changes until that point was reached.
Just remember you are altering a Victory Condition, not aggression. In other words it will not make everyone attack one another immediately, but will make each Civ pursue conquest on their own terms.
If you want aggression, the best way of doing it is to cramp the civs (this shifts civs into a CLOSER distance category when they consider any aggressive action and also increases the chance of Conquest being chosen as a victory path (or used to as of G+K, have not confirmed via code in BNW yet, too many things to look at and to much code to go through).
The main reason why peoples ideas of aggression vary post BNW is that there are certain settings which increase/decrease its likelihood.
For example people always mention Shaka, his war approach rating is high (and can be up to 10 or 11 if he rolls high on the RNG), additionally some of his other AI stats are geared towards warfare. Alternatively he could roll low and become a lot more passive.
The Map Size and Number of Civs is a big factor. Civ density is not preserved between Map Sizes, people playing on HUGE maps are likely to experience the least aggression because everyone spawns further away from each other then on any other map. Once borders begin to grow and touch this changes, but as the AI is not as expansion happy as it was this does not always happen.
Finally Civ choice. As there are so many Civs right now, and most people seem to play on standard maps, the chances of getting more peacfull or less expansionistic Civs is actually quite high. If you want aggression, choose some Civs with high base values for expansion, then choose some with high base value for Aggression. The result will be a greater degree of aggression then players are used too.
There is more but this post is already long enough
Hope this helps
BTW Note that Civs pursuing a cultural victory will keep city number low, additionally Civs with a low number of cities are more likely to go Culture (or were prior to BNW, have to confirm when I have time). AT some point I will post the code (and interpretation) that govern the choice of Civ Grand Strategy (ie Conquest, Culture etc), be aware that some of them have more specific criteria then others (Ie some are fallbacks just like some Civs do not have a start bias so that there will always be plots available during seeding).