Can you predict the outcome if Okonkwo didn't win the wrestling match that he was in when he was younger? Would he be viewed as strong and powerful? How does this outcome show how culture affects social status and relationships?

It's safe to say that Okonkwo would have turned out very differently had he lost the wrestling match. Okonkwo's defining characteristic is pride, and a desperate desire to distinguish himself from his father, who was famous for being lazy and in debt. Okonkwo craves adulation and respect, and his defeat of the Cat when he was eighteen helps him attain high status in the village. It is through this victory that he is able to win the heart of his second wife, Ekwefi.
Had Okonkwo lost, he would not have attained high status in the village (at least not as quickly), but also possibly it might have caused him to lose some self confidence and, perhaps, some of his respect for village traditions. Okonkwo's status in the village is derived entirely from his adherence to tradition, even when following those traditions comes with great personal cost (as with his participation in the killing of Ikemefuna). This is why Okonkwo is so opposed to the Christian missionaries. In undermining the traditional values of the village, Christianity seeks to upend everything that made Okonkwo who he is. Had he lost the match when he was a boy, he might have been more welcoming to the missionaries when he was a man.

If Okonkwo had never won the wrestling match against Amalinze the Cat at the age of eighteen, his social status and reputation in the community would have been low, or at the very least, just that of an ordinary villager. Okonkwo's victory in that particular wrestling match defined his adult life and guaranteed that he would be a respected man. The wrestling match itself was personally important for Okonkwo, as it symbolized his separation from his father in terms of reputation, social status, and personality.
The fact that Okonkwo was at an age of transition from boy to man when he won the wrestling match, his victory also symbolized his entrance into manhood. More importantly, it showed that he was a different kind of man than his father. In the Igbo culture, social status and reputation was very important, so the winning or losing the wrestling match was crucial in shaping how Okonkwo was perceived within the community for the rest of his life.