Tried the strategy today, with some success - although I think I was lucky, with only lions to contend with. Further good fortune involved finding copper one tile NE of my capital, allowing me to wipe out two neighbours and reduce the other to one city. Think I may have allowed another neighbour to grow too big, alas. Oh, and no one likes me...
hehehe, not too much too fast. impressive start for you, but take out one neighbor before they get going early... if you have particular success and keep most of your forces alive and have a shot at another neighbor in the immediate vacinity (with one city), then no problem going after them too... but when it comes to whether or not your neighbors like you, there's a couple things that i do to help that.
1) taking them out very early prevents anyone from truly establishing any relationships that might make another neighbor upset at you. hence the reason to take out only one in the beginning, 2 if your lucky to do it swiftly. if you keep going, you'll start getting people upset and you'll probably hurt your economy and research by blowing up to quick.
2) establish buddhism or hinduism early on. get it spreading... you'll often get +4 favorable intensions from neighbors who share your religion. they take it much better when you march. use a prophet for the religious wonder asap... it helps to spread you religion.
3) don't establish cities right on the border of a neighbor unless absolutely necessary (i.e. resources you must have). and if you do, make sure it's well fortified or your neighbor will want to take the city from you.
4) keep your military strong. on prince and above, your neighbors can smell blood. if you're behind the curve either in research or in the size of your armies, you can bet they'll be coming, friend or not.
the next opportunity i use to conquer is after the oracle gives me iron working. that's also when i find iron on the map and send a few dudes out there to act as sentry and secure the area. if it's vital, you can also daisy chain a few units along the path your settler will take.
note that you can settle directly on top of the iron and just build a road to speed along your access to it, but that's optional. once you have a swordsman advantage and neighbors who "love their brothers and sisters of the faith", then go to work again.
if i get it going right, this ALWAYS works for me... are there any thoughts on adding or improving on this? let me know!