If the veterancy thing works as it did in Civ IV in Civ V, I can see it becoming problematic in a sense that it has little or no effect on gameplay.
Problem in Civ 4 was that units became obsolete way to quickly. Even if you level up your swordsman to have like the stregth 5 promotion, it couldn't do jack shoot against a rifleman. Makes sense that way, too. On top of that, your units ended up dying long before they accumulated any significant amount of promotions, and having only 3~4 promotions still left you with a decent chance of getting beaten by the same unit with no promotions. Even if you were lucky enough to keep a unit alive for 5+ promotions, it still got killed just as easily by specific counters.
If Civ 5 has unit upgrades (eg swordsman -> maceman for 40 gold), then I guess the problem would be partially solved. But the unit upgrades can get a bit unrealistic; experience gained as a swordsman might apply when they give you maces, but you'll be starting from scratch when they give you rifles and machine guns - feels a bit unrealistic that the promotions you received earlier would carry over.
Unless Civ 5 has a way to make units effective for longer or give promotions a major boost in stats, I don't think it will have such a huge impact on gameplay.
Depend on the type of map and difficultly level and leader.
Try Boudica of the Celts on a Medium map, Epic or marathon speed.
My friend has a Gallic Warrior with 13 promotions, 3 were from a leader.
Dun gives you Guerilla 1, Barracks 3xp, vassalage +2xp, Theocracy +2xp, Usually 1 Great general by then +2xp, Boudica is Aggressive Charismatic, so, Combat 1, and cheaper upgrades. 9xp= 3 upgrades, 1 more xp for the 4th, you get combat 1 and guerilla 1 to start with. Take Woods 1,2,3 and get that 1 xp for Guerilla2.
That's 6 promotions right there, and easy to work for the rest. Capture workers, as the AI doesn't react when you are 2 spaces away from them and have woods 2.
You have the best defenses for out of city attacks, and gain xp fast to add city 1,2,3 later, add a leader and you'll gain 3 more promotions, one will be leadership for 100% xp earned, and tactics for a higher withdrawl rate, which stacks with guerilla3 when you get that.
Celts are gods of early terrain combat.
If Civ 5 is like this, it will only slow down, because, we have fewer units.