Well, Rowling said in HBP that every Prime Minister is in touch with the Minister of Magic. So Churchill would have been in contact with whoever was in charge, starting when Winnie became P.M. in 1940. (How much cooperation there was, I don't know--Fudge and Scrimgeour were pretty patronizing--but I can't see Churchill putting up with patronizing contempt for long. (Or going into meetings with wizards without some way of protecting his mind and memories, come to think of it. The man was NOT stupid.)
As for Hitler, it's never been said what kind of influence Grindelwald had. Fan theories have varied from Hitler being Grindelwald's overly ambitious apprentice to being his Muggle puppet (someone Grindy was using as a front who was implementing his policies) to someone who had heard the attitudes of the wizarding world toward Muggles and decided to apply those attitudes to racial, religious and social groups that he hated and feared. Rowling has never said.
That there is a connection between the two wars, she made clear in HBP. The wizard's war with Voldemort necessarily means death and destruction for Muggles as well; it's reasonable to conclude that Grindelwald's forces would be no more considerate than Voldie's at destroying people who could not, magically, fight back.
Furthermore, there's also this (http://www.eveningprophet.com/faq/view/198):
6.10.2 Do Muggle wars and Wizard wars feed off each other?
According to JKR, yes.
And this (http://www.mugglenet.com/jkrinterview3.shtml):
ES (Emerson): 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.
[N.B. Obviously she changed her mind about Grindelwald dying in 1945. But I think the rest still applies.]
:::
MA (Melissa): Do they feed each other, the Muggle and wizarding wars?
JKR: Yeah, I think so. Yeah. Mmm.
MA: You've gone very quiet.
[All laugh; JKR maniacally]
***
So...yeah. It seems clear that Rowling intended WWII and the War with Grindelwald to be intertwined.
I just don't think she thought out all the implications of that.
The War With Grindelwald, World War II and Rowling
As for Hitler, it's never been said what kind of influence Grindelwald had. Fan theories have varied from Hitler being Grindelwald's overly ambitious apprentice to being his Muggle puppet (someone Grindy was using as a front who was implementing his policies) to someone who had heard the attitudes of the wizarding world toward Muggles and decided to apply those attitudes to racial, religious and social groups that he hated and feared. Rowling has never said.
That there is a connection between the two wars, she made clear in HBP. The wizard's war with Voldemort necessarily means death and destruction for Muggles as well; it's reasonable to conclude that Grindelwald's forces would be no more considerate than Voldie's at destroying people who could not, magically, fight back.
Furthermore, there's also this (http://www.eveningprophet.com/faq/view/198):
6.10.2 Do Muggle wars and Wizard wars feed off each other?
According to JKR, yes.
And this (http://www.mugglenet.com/jkrinterview3.shtml):
ES (Emerson): 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.
[N.B. Obviously she changed her mind about Grindelwald dying in 1945. But I think the rest still applies.]
:::
MA (Melissa): Do they feed each other, the Muggle and wizarding wars?
JKR: Yeah, I think so. Yeah. Mmm.
MA: You've gone very quiet.
[All laugh; JKR maniacally]
***
So...yeah. It seems clear that Rowling intended WWII and the War with Grindelwald to be intertwined.
I just don't think she thought out all the implications of that.
But it could make an outstanding AU.