No, you cannot be thrown under any circumstances until 6 frames have passed. For normal throws, the game won’t even let you attempt to throw until 6 frames have passed. Since most normal grabs are 3 frames, that theoretically makes it 9 frames where you cannot be thrown after waking up in most cases. Well timed command throws will be able to grab right on the 7th frame after you get up though.
9 frames might sound like a lot, but it’s really only 9/60ths of a second, or about .15 seconds. The vast majority of us don’t have reactions that fast, so throws are still a powerful part of any good mix up on a rising opponent.
RCing a move adds about 3 frames to it. With this in mind, wake up RC moves that either hit in 3 frames or less or leave the ground in 3 frames or less or totally immune to throws. Wake up moves that are off the ground or hit within 6 frames should be immune to normal throws only.
Examples would be Rolento’s RC KKK hop, Mai’s RC wall dive, Shoto RC hurricane kicks. These are all really buff wake up moves and effectively kill almost any wake up mix ups you might have. Counters to these RCed wake ups are totally character dependant.
Examples of wake up RCs that should be immune to normal throws only would be Chun RC legs, Vega RC rolling claw, Eagle’s RC spinny move, and Todo’s RC grab. Keep in mind you should also be getting reversals.