It’s possible - J.K. Rowling hinted the two wars ‘fed each other’.
In an interview, J.K. Rowling says that the wizarding war with Grindelwald and World War II were times to be parallel, and she thinks there’d be a wizarding war at the same time. She doesn’t say whether Grindelwald was directly involved in World War II, and she avoids saying much more.
ES: You don’t have to answer but can you give us some backstory on him?
JKR: I'm going to tell you as much as I told someone earlier who asked me. You know Owen who won the [UK television] competition to interview me? He asked about Grindelwald [pronounced "Grindelvald" HMM…]. He said, “Is it coincidence that he died in 1945,” and I said no. It amuses me to make allusions to things that were happening in the Muggle world, so my feeling would be that while there's a global Muggle war going on, there's also a global wizarding war going on.
ES: Does he have any connection to --
JKR: I have no comment to make on that subject.
MA: Do they feed each other, the Muggle and wizarding wars?
JKR: Yeah, I think so. Yeah. Mm.
MA: You've gone very quiet.
[All laugh; JKR maniacally.]
MA: We like when you get very quiet, it means —
ES: You’re clearly hiding something.
- Leaky Cauldron interview (16 July, 2005)
There does seem to be a connection, but it’s not clear whether it’s a direct one or if it’s a more general “all the world was in turmoil at that time” connection. From what she says, it’s possible J.K. Rowling just thought it an interesting out-of-universe allusion, and wanted to time it so that it would be wartime for wizards as well, without active involvement from Grindelwald, whether or not he was directly involved in causing it. It’s also possible he was directly involved, she doesn’t want to say.