Seeing the results of my own game (1466 dom victory but the last 40 years were settling the voids and waiting border pops), i can confirm that a very early rush with an army of only immortals is powerfull indeed.
The very nice thing is that when opponents start to be a bit tougher (cities with culture at 60% + wall, protective), you have plenty of combat IV or V immortals that can handle that. The heavy loss are not a problem, as those guys are so cheap. I think i got more than 10 GG (all settled spare the medicIII).
The only city before longbows i had to wait for cats was Wong capital (protective) which was on hill and with 10 defenders.
The RE economy (razing
) seems to work and dont slow you down. A very nice trick is to spam missionaries each time you take a shrine, that helps a lot. Razed 20 cities or so.
Also i did capture the GW early which was great (razing cities means a lot of voids for barbs ), then the ToA which generated some GMs.
I was at war 99% of the time.
I did go cottages, the economy was a bit shaky (running deficit balanced by cities ransoms) but teched at good pace (lib in 1050AD). I would have probably switched to SE if i had captured the pyramids earlier (around 1000AD too).
If Pangea, going conquest should be even easier, here i had brennus on an island by himself.
Edit :
Point noteworthy : immortals have strong bonus attacking axes and archery, not swords. Against someone like Shaka, who favor them, be carefull