sure, you can map the virtual to physical however you like including one to one such that they are equal. There are still differences vs having the mmu off, each and every access has to go through the mmu and be looked up and converted (even if one to one), these tables themselves are in ram as well and that takes time, there is a little cache to help (TLB) but pretty small. Then there are the other settings in the mmu, cachable or not, protection which may require an additional lookups within the chip which may or may not take extra clock cycles.
So purely from an addressing perspective, sure the virtual address and physical address can be the same for the whole address space. there are some bits in the mmu table that replace some bits in the physical address and you can set those to match for some or all of the address space.