Hi - exactly this happened to me. ELCS for 1st DC because of severe primary tokophobia, and my waters went ten days before my ECLS date.
It was fine. If you go in as SOON as you think something is happening, be it pains, odd twinges, a show, waters going - anything - then they will almost certainly have plenty of time to fit you in to theatre. technically it will be an EMCS, but that's just because it won't be on the date you have booked.
A very small proportion of women labour very fast - but it is very small, and if this is your first, it's even more unlikely this will be you.
The key thing is to get in there early. Try and make sure you have this written on your notes - that you DO NOT WANT a trial of labour or any such if things kick off before your ELCS date. Standard advice for labouring women is basically to wait as long as possible before coming in to hospital. You do the opposite. My (brilliant and sympathetic) community MW told me to ignore anyone telling me to have a warm bath, or 'see how it goes.' Get in there, and get on the list for theatre. It really won't matter if you have to wait because of emergencies if you are there early on. Some people love to scare those with booked CS's by telling them they aren't guaranteed a slot etc. Non emergencies will always have to wait for emergencies. That's entirely reasonable! and those are normal circumstances.
I had to wait about 24 hours from the point my waters went to going into theatre. It was fine (I did get bored and hungry and thirsty as I was nil by mouth for a good 6 or 7 hours! but really, that's no big deal).
My CS was a lovely, happy birth, and me and my DS were fine. I recovered very quickly - much more quickly and comfortably than other mums who had instrumental births btw - and DS was 100% breastfed.
Good luck.