One consequence could be that his friends worry about him a great deal. They might go on a search for him, which could put them in danger as well. After all, they care about Naruto deeply and won't just let him disappear without trying to find him.
On a positive note, Naruto might grow stronger during his time away. He could encounter new challenges and learn new skills or jutsu that he wouldn't have learned if he had stayed in the village. However, he also risks getting lost or losing his way, both literally and metaphorically, without the support of his friends and mentors.
The village might be in chaos. Naruto is an important figure in the village, and his absence could lead to a lack of morale among the villagers. Also, there might be some who take advantage of his disappearance to create trouble in the village.
He could become stronger on his own. Away from his family, he'll have to rely solely on himself. This self - reliance might push him to train harder and unlock even more of his 'godlike' powers. For instance, he might find new mentors or training methods that his family would not have allowed.
He might miss out on some crucial training. Jiraiya has a lot of knowledge and skills to pass on, and by running away, Naruto could fall behind in his development as a ninja.
He might face a lot of danger on his own. Since he's running away from Kushina who would usually protect him, he could encounter stronger enemies that he's not fully prepared to face.
One possible reason could be fear. Minato is a very powerful shinobi, and Naruto might be scared of him for some reason. Maybe he has heard stories about Minato that made him afraid.
Maybe he's running away from the pressure in the village. There are always high expectations on him, and he might feel suffocated and need some time alone to figure things out.
One possible reason is she's had an argument with her friends and feels she needs to get away to cool off.
It could also be due to a particularly bad encounter with someone in the village. For instance, if he was bullied severely by some older kids and he felt that there was no one to protect him. He might have thought that running away was his only option to avoid further harm.
Naruto could end up getting lost, both literally and metaphorically. He might lose his way in the shinobi world, not having Minato's guidance. He could make wrong decisions about his training, alliances, etc.
They might run away to avoid a conflict that their villages are about to be dragged into. Naruto and Sasuke, being the powerful ninjas they are, don't want to be used as tools in a war, so they decide to run away.
Perhaps he is running away from danger in Konoha. There could be a threat that he believes he can't face directly in the village, and he thinks Whirlpool might offer some sort of sanctuary or a way to become stronger in relative safety.