Yes, there are certain habits and certain inclinations that are being built up through lifetimes, or even in choices that one makes. There are certain things about personality even up to the level of an arahant.
For example, in the way of the senses, the body has been used to certain flavors, certain choices in terms of cuisine. That's one aspect of personality. They have their favorites in the way of how the body deals with certain things in relation to consumption of food, and things like that.
The second aspect is how they grew up in a culture as well. Of course, with the arahant, they don't consider culture to be something that is part of their personality. It's just ingrained within that personality. They don't take it to be personal, they don't take it to be their selves.  Even in the time of the suttas, everything was in ancient north India. So, everything that everyone understood, was through that cultural context. So, there were certain things there that built up that kind of character. The Buddha and all of his cousins were of the warrior class, so they had a certain kind of understanding of how to behave, how to interact.
But it doesn't make up any more of a being, any more of bhava. These are all accumulated tendencies that arose prior to full awakening. So there may be effects of certain understandings that were there, that would just be neutral in the sense of not having any wholesome or unwholesome effect. They're just ingrained within the personality.
There can be characteristics like a certain inclination towards a type of food, towards a type of geography, or weather, or location. Despite all of that, when one is fully realized, even though that's still present, it's not personalized. It's not in the way of I need that, or I require that. They just know that the body has become used to that. And if it's there, it's all well and good, if it's not there, that's okay too.
So long as you understand that the character of a person is built up through various experiences, through various cultural traditions, and through various upbringings through one's parents, elders, and teachers and so on. The difference with an arahant is that one takes those cultural contexts and takes all of what has brought up that character, to be personal.
In the suttas you have different types of arahants. Some arahants are quite stern or driven towards asceticism. And other arahants are quite gentle and prone to seclusion. And you have arahants who are more like teachers and are prone to teaching. These are all built up because of past kamma. Kammic inclinations that were built up in previous lifetimes, and in previous choices in the present life, but those are helpful in the context of how they can  better deliver the dhamma. Or serve the dhamma and people in being able to  provide the dhamma to them.