The question might better ask one to explain whether Homer presents a believable case for his proposition that the actions in Book I of The Iliad are controlled by the gods. The agreement or disagreement of a 21st century reader would be immaterial as it would not be text-based opinion but rather personal-belief based opinion: the pagans among us would probably agree, the others would probably disagree. So the question that can be answered from the text is whether Homer is convincing in trying to win agreement with the proposition that the gods were in control of events in Book 1.
One of Homer's first statements is that Apollo ("son of Jove and Leto") was angry with Agamemnon ("the king") for the reason that he ("the son of Atreus") had "dishonoured Chryses" Apollo's priest. Homer's next step is to show Chryses appeal for his abducted daughter to be returned to him. First of all, Chryses does not storm in and demand her release in a rage. On the contrary he presents himself respectfully and in an honorable official capacity with the symbol of his full power as Apollo's priest displayed by the scepter of Apollo that he carries. In this capacity, with this visual reminder of his connection to Apollo, Chryses summons the laws of the land and offers a rich ransom in exchange for the return of his daughter. Second, Chryses does not curse Agamemnon and the Danaans, rather he blesses them by saying: "may the gods who dwell in Olympus grant you to sack the city of Priam, and to reach your homes in safety."
Next Homer presents the prayers Chryses makes in private in the temple of Apollo after being denied what he could rightfully claim, a claim confirmed by the reception all the Danaans except Agamemnon gave his offer of ransom. Homer tells that Chryses asks that Apollo avenge the Danaans for his tears shed for his daughter. After that Apollo sets off into action and, by Homer's account, does indeed avenge the tears of Chryses, which injustice and hard-hearted rejection of custom and law caused him to shed.
Based on the cause-effect relationships that Homer sets up and based on the depth of character portrayal that Homer establishes--giving such clear pictures of the principle characters based on their words, tones of delivery, attitudes, and actions--it seems quite reasonable to conclude that Homer does provide enough sound evidence in the text to substantiate his proposition that the gods, specifically Apollo in the beginning of Book 1, were in control of the events that followed Chryses failed negotiations and subsequent prayers.