32-bits run fine on devices with a 64-bit CPU, just as it was stated during the announcement of the iPhone 5s and Apple's first mobile 64-bit chip. The problem is that 32-bit apps won't be able to take fully advantage of newer CPUs. In terms of basic performance you should be able to notice the difference without even that extra support, but in-app most of the advantage would come with the transition to 64-bit support.
That's why I do think developers really need to have their apps support this. And I'm glad that Apple included this warning.
So the app will run fine, it just wont be able to fully utilize the hardware. I feel like a better message would be "This app may perform slowly" or something along those lines, not a message easily interpreted as "This app will make your whole phone slow"
Its a bit deceitful really.