Without swap, you mean without virtual memory or without a swap partition/file?
Because even without a swap partition/file, the whole executable will not block physical memory, but will page in/out as needed. And whole sections of it will never be loaded at all.
Yes, any mmap'd file will be swapped in on demand, when a page is first accessed, it will not all be copied in physical memory at once. In case of memory pressure, pages will be removed from physical memory ("swapped out"), since they can be loaded back from the file again when needed.
Since the executable is mapped read-only, the pages loaded in physical memory can also be shared between multiple instances of the process.
Because even without a swap partition/file, the whole executable will not block physical memory, but will page in/out as needed. And whole sections of it will never be loaded at all.