I haven't had a problem using this strategy without construction. In fact, I wouldn't delay that long because then you might be facing longbowmen.
I think the key is to scout your target's entire territory to identify all his resource. If you have an enemy without horses or metal, go for him first. Archers don't stand a chance against city raider swordsmen. If your enemy does have the resources, position groups of chariots before declaring war to eliminate those strategic resources immediately once you declare war. Also, start with the capital if at all possible to eliminate their highest product city.
I had great success last night on monarch playing as Rams. I had stone so I built the pyramids planning on getting feudalism that way, but suddenly I noticed that nobody built the oracle and I was about to finish with monarchy. So I tree chopped the oracle on the same turn I finished monarchy and got feudalism.
I was a little late starting my war because I ended up building both wonders. My capital was up to 11 at this point, so I whipped a swordsman every other turn until my capital was down to five. Combining those with my other troops, I geared up to get some vassals!
I positioned my chariots to pillage Carthage's only strategic resources. I noticed his cities were weakly defending with 2-3 archers per, so I positioned my melee troops to take his 2nd and 3rd largest cities right away, then to combine those and take his capital.
I took his top three cities quickly, leaving him with three scrubs. He capitulated. Sadly, and coincidently for him, he got longbowmen the turn or so after he lost his capital and capitulated. This shows that the delay in my war almost made me miss out as he would have ruined me had he gotten longbowmen. Plus, this shows that if I would not have had feudalism to vassalize him, I would have had a bit of a tough time finishing him off.
Next, I made the same preparations against Cyress. Fortunately, I was able to take his capital first due to the shape of his empire, which really knocked the wind out of him. Plus, almost at the same time I took his second largest production city. The next two I took sequentially as I was wearing a little thinner by this time (some of my troops hadn't even fully healed from my first war).
I took his top four cities quickly (including his capital of course), leaving him with four scrubs. He capitulated.
Now I have two vassals with seven cities between them and lots of so-so extra land for them to grow back. They still have a bunch of tech I don't have, and they are willing to trade with me. This is great as compared to wiping them out (where you can't get their tech). This is also great as compared to not finishing them off and only suing for a couple techs and then having them not trade with you. Plus, I now have happiness bonuses in all my cities which address war weariness for my next war.
I noticed that Spain and America still don't have feudalism so I am going to move my troops out and try to make one of them vassals, or at the minimum raze some of their cities and pillage everywhere
By the way, I was last in score before I attacked Carthage and first in score with a 20% lead after I finished with Persia

So chalk this one up as a success.