Yes, there might be. There are a vast number of fanfictions out there for various combinations of popular culture elements. Since Highschool DxD has a large fan base and Godzilla is an iconic figure, it's not unlikely that some creative fans have combined the two in a fanfiction. You can try searching on popular fanfiction websites to find such works.
One common theme is power. Godzilla is extremely powerful, and in the DxD universe which also has powerful characters, exploring how his power compares and interacts is a big theme.
Godzilla might see the pregnant Muto as a threat. After all, Mutos are his enemies. So he could start hunting it down to prevent more Mutos from being born.
Naruto would probably be both amazed and a bit scared at first. But being Naruto, he would quickly jump into action. He might try to use his rasengan against Godzilla, thinking it could do some damage. However, he would soon realize that Godzilla is much more powerful than he initially thought and would have to come up with a different strategy, like using his speed to avoid Godzilla's attacks and find its weak points.
Shinji would probably be terrified at first. He's already hesitant and scared in his normal battles, and Godzilla is much larger and more intimidating than the Angels he usually faces. Asuka would likely be more aggressive, thinking she can take on Godzilla with her Eva. Rei, on the other hand, would be very calm and observant, trying to understand Godzilla's nature. Misato would be in a panic initially, but then quickly start strategizing on how to deal with this new threat. Gendo would see Godzilla as either a new opportunity or a major obstacle depending on his long - term plans.
Some of them might be amused. For instance, Hulk could find it funny if Godzilla was shown as being weak in the fanfiction. He might laugh and say 'That big lizard not so tough!'.
Some of them would be amused. Hawkeye might chuckle at the outlandish scenarios in the fanfic. Black Widow would be more reserved but still interested. She'd be quietly observing and thinking about the implications of the story. Captain America would try to find the moral of the story, if there is one, as he always does.
Godzilla could be a new kind of threat that the characters have to deal with. Since Highschool DxD has a lot of supernatural elements already, Godzilla could be seen as an even greater supernatural force. It could be that a dark magic spell accidentally brought Godzilla into their world.
Well, in some fanfictions, Godzilla's presence in the Highschool DxD universe might disrupt the power balance. For example, Godzilla's atomic breath could be a huge threat to the various factions in Highschool DxD. Some fanfictions might explore how the characters adapt to this new and extremely powerful entity. They might try to find a way to communicate with Godzilla, like using magic spells or special artifacts to bridge the communication gap between them and the giant lizard.
One idea could be that Issei is a huge Godzilla fan and he finds an ancient relic related to Godzilla. This relic starts to influence his abilities and his relationships in the Highschool DxD universe. For example, it could make him more aggressive in fights but also attract the attention of some powerful and mysterious beings who also have an interest in the relic.