We actually tested this. Both on and off wifi, my phone takes a total of about 31 seconds from the killing blow until I can get into the next battle. I have a Google Pixel XL on Verizon’s network.. probably the best android out there from a hardware perspective.
Gideon was using his iPhone 6 I believe.. His average finish to start load was about 15 seconds. So he was about twice as fast as my loads. So yeah, it matters big time. And if you are racing that accounts for at least 2-4 games per hour assuming you have a strong deck. Pretty sure the game is just faster on the apple platform. Not exactly sure why.
My Galaxy S5 did the same thing… I can take calls, switch applications, let the phone go to sleep for hours, and still have the game stable on the Pixel… loving it!