No - I don’t think they can.
Assuming they’re at all sincere in the first place (with both Trump and Musk, there’s no telling), they’re all fired up about it now because they’re still on the outside looking in. But soon enough, they’re going to be in the same position as every other government body - they’ll be cutting deals and making exceptions and trading favors and bowing to pressure and breaking promises and blame-shifting, and they’ll fail and end up just another part of the swamp they claim they’re going to drain.
The real problem though is the damage they’re going to do along the way, since they’re all ultimately just self-serving, lying sacks of shit - loathsome even by the already low standards of politics.
They’re already the epitome of swamp whether they accomplish their goals or not. They literally campaigned on tax cuts for the rich.
Of course they can, thats easy. Can they do that and still have a functioning society with infrastructure in 5, 10, or 15 years? The thing about ripping pieces from the machine is, those pieces all do something in an additive manner.
As far as I know they have no power whatsoever as they are not a government agency and do not control the budget nor the purse strings. However, if enough Republican Congressman don’t give a shit, and bet on their electorate not being smart enough to pay attention, well then maybe they’ll succeed.