Generally yes - at least that's probably the most common way of using them.
It's not mandated that way in the UML spec; it allows a more general use of state machines. For example, a Final State can be used to signify the end of a behaviour thread within a region if the state machine has >1 regions. Or a state machine can be used to define a protocol instead of an object's lifecycle.
Some variants (profiles) of UML do enforce the behaviour you describe, for example UML ejecutable.
I'd probably turn the question on its head and ask: would it be useful to you if the state machine did define the object's lifecycle? If so then just use it that way. If you need to formalise then you podría define a profile. But it's equally fine to just agree informally in your team.