From my experience, if the following two conditions are met, you should continue. if not you should quit:
1) Are you ok with not coding and just have a technical vision and dealing with people constantly ?
2) Does the CEO respect technical part of the project ? that means he doesn't think that he can imagine anything and then the CTO will do it with his team.
Let me explain each point:
The first one: as a CTO most of your time is spent on:
- [Hiring] this part will probably take 20% to 30% of your time. you have to interview them technically and be able to sell your company and motivate them.
- [Communication] Communicating with the CEO and other key roles: this is everyday, you have to be involved in every decision concerning the product. and you should be able to explain clearly why you are against or for a feature in the product (this one takes maybe 30% to 40% of your time!)
- [Technical] Macro architectural decisions, code revision, etc.this is paradoxically the easiest part ! it should not take more than 20% of your time.
- [Management] Making sure that developers are motivated enough, talking to technical team every morning and trying to understand their feelings and vision and deciding if they are in line with the culture of your team. this part should take 20% of your time. if it takes more than that, that means that you didn't do the hiring very well. so you should spend your energy on firing and hiring again.
The second one: Does the CEO understand that technical decisions are vital for the project so he has to include you on any business decision ?
If yes, then it is a good news. but if the CEO is that old school guy who thinks that any idea can be implemented by engineers and the CTO is the responsable for any non respected deadline then just run. quit, don't even try to change his/her mindset cause you cannot. usually it is really easy to figure out that the CEO respects technical part or he just pretends to respect.
Hope that helps :)
PS: Most people (myself included) cannot dive into code and dealing with people at the same time. When I am coding I don't even here what people is telling me. so I cannot be good at management. that's why I think that a CTO should not code at all.