Under memory pressure, the kernel evicts less popular pages from memory. If a page has been mapped from a file, it is dropped (if dirty, then it is written out first). If it is needed later, the kernel can read it back from the file. If a page is anonymous (read: heap page), then there is no backing file and the kernel copies it to swap before dropping it. This is swapping.
So, what happens if you disable swap and the kernel is low on memory? What can it evict? Anonymous pages cannot be evicted: there is no swap to put a copy in. The only choice the kernel has is to evict pages that are mapped from files. Those include pages mapped from the executable. You don't eliminate stalls by disabling swap, you just move them elsewhere: the kernel will page out code and your app gets paused whenever the execution flow hits such a page.