Absolutely, yawning at you is definitely a form of a greeting or a hello with rats! Before my husband and I adopted our first rats, I did a ton of research via books, articles, etc, and again and again I read about yawning as a form of greeting. It is a strong theory that rats DO do this to greet or say hello to us..an affectionate gesture towards their humans.
My ratty boys have always done this..and especially with the forearm stretched out towards us, it just makes our day. My husband will call over to me, after he has gone to say hello to our current boy Achilles, and say, "Hey, I got a yawn greeting AND forearm stretch!"
I can tell the difference between when they are just yawning because they are sleepy or just woke up, and when they are doing an affectionate greeting because the "hello Mom" yawns I get almost seem to be a quick "fakey" one with a quick arm stretch and not a genuine "I am just waking up" type yawn, if that makes sense? Like they are going out of their way to do a "yawn gesture" with an arm stretch rather than a full on, "I am sleepy" yawn.
Other times, it does look like a genuine yawn, but something tells me that no matter what the yawn and arm stretch may look like, I am convinced they are saying a hello and expressing an affectionate greeting toward us, especially when they are directed the gesture right toward us, when they see us. So, yes, I totally agree with the theory, 100 percent.