No, and you'll have to ask Intel :)
An (over)simplified explanation would be: if we're in protected mode, a bit in the descriptor to which cs points determines if the CPU is running in 16- or 32-bit mode. In real mode, there's no such bit.
You can use 32-bit instructions with the CPU in 16-bit mode. You can even use 32-bit addressing modes - but ordinarily, offsets are limited to 64k-1 (there's a workaround for this - "Flat Real Mode").
What is it you're trying to do?
Best,
Frank