Yes, but it's not as useful as it is to a modern person, because if you're the only person who owns a clock then your life will have very few situations where k

Yes, but it's not as useful as it is to a modern person, because if you're the only person who owns a clock then your life will have very few situations where knowing the time exactly and reliably matters -- so you only own one if you have some specific use-case where you care about exact time. The benefit of owning a precise and accurate clock becomes much greater if you are frequently interacting with other people who also have precise and accurate clocks (such as operators of railways), and at the point where most people in a society have an accurate clock then it becomes a default assumption that scheduling can be done by time and you will find it increasingly difficult to be without one. (I think the smartphone is currently going through a similar transition -- right now it is definitely still possible to live without a smartphone, but an increasing number of organizations are now starting to act on the assumption that every person they deal with does have one.)