No.... my second paragraph illustrates exactly what I'm getting at. You're ill-appreciated sarcasm aside, let me clarify it a bit more for you.
Gandalf, as far as the reader's suspension of disbelief is concerned, is real. As are Hobbits. As is the Witch-king of Angmar. Let's say that during their confrontation Gandalf stood up, bent over and started shooting Hobbits out of his [censored], whereupon one got logded in the throat of the Witch-king and he started choking on the Hobbit's furry feet, finally spitting him out and ultimately turning to flee, knowing he'd been bested by a cagey Wizard's anol, Hobbit gun.
How's that, how do you think that would fit into Lord of the Rings. Would you be fine with it?.. because eveything else is also make -believe?
See what I"m getting at ... even though it's fantasy and were being asked to believe and emotionally connect with something WE KNOW isn't real, we do.. because the story isn't asking too much from our own common sense that we've let be stretched and pulled to fit into the writer's narrative.
Your first paragraph gave me a good laugh and to answer your question, no, I would not be ok with that scenario occurring. However, that is not the case in the Lord of the Rings and Skyrim. We don't have hobbits flying out of Gandalfs' ass and we don't have Dovahkiin shooting laser beams from his mouth and flying ponies into the sunset. In actuality, Skyrim is providing us a completely new narrative and setting to explore for on our own, while also giving us some abilities to tinker with, dragon shouts being one of them. It's a fantasy world and your topic post is basically questioning the validity of dragon shouts in a fantasy world.
Compared to Skyrim, how is Lord of the Rings more emotionally engaging and believable? How is it that we can have super-sized Elephants walking around or Arwen summoning a wave to wash away Ring Wraiths as believable, but a character of exceptional power, a person that holds the power to speak the tongue of dragons and use it against them, is lame, cheesy, or far-fetched? I know i'm beating a dead horse here, but where are you drawing this imaginary line and suddenly coming to the conclusion that Dragon Shouts just aren't believable and will detract from the immersiveness. If anything, it's adding to the overall lore of the game and immersiveness because the Dragonborn are people capable of utilizing Thu'um. If they don't include it, it detracts from immersiveness and lore.
If your original post had just been the first paragraph it would have been a valid concern, but when you go off in the second paragraph comparing Dragon shouts to Tolkein's fantasy world it completely undermines your original statement. Both worlds are so far from our world, you can't suddenly start drawing parallels and determine that Tolkein's is more believable. Skyrim and LOTR are practically the same setting when you look at it. We've got dragons, giants, trolls, elves, humans, dark dungeons, diverse environments, etc. Arwen's ability to summon a tidal wave by whispering words can even be paralleled to Skyrim's dragonborn summoning bad weather to rain on the dragon's parade, but oh wait, I guess that's a little too cheesy.
To each his own I guess.