Can an autocratic leader amass power without fostering a cult-like relationship with his/her followers? What role does emotion play in this process? Are the religious more likely to favor autocratic rule?
Hypothetically it is possible, however the absolute power ultimately create a cult-like followership in the end, but of course it is more likely to get your fans before you come to power, but it is possible after that. Just take a look at my beloved country (Hungary) and it's prime minister.
Look at the writings of Manfred Kets de Vries who links organisational culture with psychopathology of its leader. He explains the mechanisms at play. Extrapolate that and you could get to your hypothesis.
As to the culture of countries, look at Hofstede’s writings where he decribes them along several axes like masculine-feminine, low trust versus high trust etc. That would cover your second question as to religion.
I believe it is possible for autocratic rulers to amass power without a cult of personality, however, once in power, it is likely that a cult of personality will form to consolidate power, remove opposition, and strengthen perceived public support. This can be seen with Stalin for example who used his early position as Party Secretary to control meeting times and agendas, to maneuver around his opponents while remaining relatively unknown. Once in a strong position of power, he consolidated it by beginning to work on his personality cult. An early venture of this was by providing Trotsky the wrong date for Lenin's funeral while taking lead in the procession to diminish Trotsky's public support while building his own. I am sure there are many other examples of autocratic rulers who amassed power without fostering a personality cult and only later worked on it, however, this was the first one I could think of. I recommend watching "How To Stage A Coup" Netflix as it briefly touches on how autocratic rulers have taken power in the past; Mussolini and Hitler mentioned as those that used their public speaking to amass power while simultaneously building a personality cult. Another potential example of an autocratic leader who amassed power without a personality cult is Kim Jong-Il who inherited power. Of course, he began a massive state program to heavily enhance the personality cult machinery, but his power consolidation was through party purges and appointing only those who closely support him. This example, however, is a very thin line; I am not sure it counts as amassing power given it was inherited and I would say it depends how you define power? Political power? Power through public support?
As for religion, I have doubts that the religious are more likely to favor autocratic rule as the notion of worshiping a God runs counter to the personality cult rhetoric that the state leader is meant to be God-like, and central to the people and state. It should be noted that I don't have evidence to back whether the religious are more likely to favor autocratic rule. Stalin, Hitler, Pol Pot, and the Kim dynasty are prevalent examples of stamping out religion or incorporating them into the state because they run counter to the state rhetoric. I doubt the religious would support autocratic rule, particularly when its incorporated into the state; who would want to see their religious belief follow Party line more than their scripture?
I would like to add: It is necessary to define what is meant by a personality cult. It is possible to distuinguish between how a person gains power within an organisation, be it a party or a government or the military, by building up a cult around them, a group of yes-men, an inside circle that takes over that organisation, and when in power they foster a personality cult around themself as a God-Ruler. There are widening circles and a hypothesis would be that the cult starts early, within a small group and that the circle then becomes wider and wider until it reaches the whole of society.
I have a suggestion that might add a new dimension to this discussion: what if an autocratic regime was run by an AI and fully-automated? Would this hypothetical regime likely be structured like a personality cult or would there be no need for such a structure?