A random number is a valid v4 UUID, provided you set the version and variant bits to the correct value. A random 128-bit number won’t have those bits correctly set (except by chance). Set them, and you’ve made a valid v4 UUID
As you say, you need to set certain bits to special values to encode a v4 UUID, leaving less than 128 bits for the payload, which means a random 128 bit number is not a valid UUID except by chance.
Second, a v4 UUID should set all remaining bits randomly. Encoding a timestamp in some of the bits is not random. Sure, you could argue these could have been randomly generated by chance, so any such UUID is not invalid, strictly speaking. Still, a collection of these v4 UUIDs don't have the properties that you would expect of random UUIDs.
As specificed, the scheme satisfies neither of these two requirements.
A random number is a valid v4 UUID, provided you set the version and variant bits to the correct value. A random 128-bit number won’t have those bits correctly set (except by chance). Set them, and you’ve made a valid v4 UUID