Good luck with that. They can barely contain Loki. You really think they'd pop out and subdue Thanos and his army? Especially Thanos with all six Infinity Stones?
its unclear. since they are powerless in the TVA. yet they would be in his universe. yet ben there they are kinda capable, the subdued Loki with no issue.. Its hard to tell
As I interpret "Loki," in any number of alternate timelines, Iron Man DID fail to take the stones from Thanos.
But those branched alternative timelines would immediately be "pruned" by the TVA.
I don't think TVA agents "cause" events to occur. They don't need to, since every possible outcome DOES occur in its own discrete timeline. The TVA just prunes any possibility that branches too far from the "sacred timeline."
So if Thanos kept the stones, he'd be shocked to see TVA agents appear, set their timeline bombs, and promptly leave. No way would Thanos get to actually snap -- the variance would be too extreme.
You'd need to have Sylvie-level intelligence to realize what was going on and escape before that timeline gets pruned out of existence.
The clear implication is that if he failed, he failed. The TVA don't step in to help, and even if they tried, they weren't going to stop Thanos. Even without all of the Infinity Stones they were no match for him, but of course at that point he had all six.
Only within their out of time office world are the stones useless. As for their batons, I'm going to have to assume that Thanos is able to resist that. They never spell any of it out, but clearly he's resistant to powerful attacks. Dr. Strange must have access to some lethal magical attacks, but Thanos easily withstood everything he threw at him. Not to mention Tony Stark, who certainly is bright enough to devise a weapon as powerful as those batons. Either Thanos is naturally resistant to such things, as one assumes, say, Thor is, or the Infinity Stones are protecting him from such attacks.
(punchline: it's revealed in the end that Bugs is wielding the pencil)
But you're right, while inspired any comics, the MCU isn't literally a cartoon. TVA's pruning baton may function like Bugs Bunny's pencil, but it's still an artifact whose powers and limitations remain unknown until Feige & co. tell us explicitly.