in turn 37 we could have our first spear ready, and i assume it will be enough (we have 3 warriors arround that point)... ...and if not, we can build them "en masse" in our second city from turn 36 on... ...and if they manage to take us out before turn 37 with 2-3 immortals... ...they are so incredible good players that we wouldnt have had a chance anyways
just do the math: worker with plainshillstart: 12 turns + 5 turns foodstuff (you need to grow to have production to get immortals out at a decent speed) + 4 turn pasture + 4 turns roads (given horses are 2 tiles away from capital)=25 turns, without loosing any worker turns to walk to destination, immortal 30 hammers (I think), lets assume a production of 5 for the first immortal, we have the first immortal ready to go in turn 31+/-... ...getting to us then takes maybe 5 turns more = turn 36+/- first immortal at the gates... ...and i still dont see an easy win of an unpromoted immortal against 3 warriors fortified on a hill, in a city, even without culture...
4 vs 2+25%+25%+25%=3,5 with culture of 20%: 3,9
if we dont suffer terrible bad luck, we would loose the first warrior but the immortal should be wounded enough to be cleaned up with our second (or third) warrior.
once we have 2-3 spears ready (which we can have around turn 40, if we delay oracle a bit, what we would do in an emergency situation like this for sure), the window of opportunity of the immortals is over (you need soooooo many of them to still do real damage, that you cripple your own buildup totally)