I don't think he can get away with making large share purchases without the IRS, FTC, or FEDS knowing about it. Especially when you're a world-known billionaire with all eyes on you like he is. I'm sure the US government watches him like a hawk. Especially him, because he's not a rabid left-wing radical like most billionaires. They hate that. He's a pretty middle-of-the-road moderate.
However, Elon Musk strikes me as a really sharp guy who knew they would respond this way or at the very least has a plan B if they did. As a matter of fact - he may have even planned it this way.
When making the purchase offer to Twitter - he threatened them by implying that if they refused his premium buy-out offer, he would unload his shares and tank the stock. The interesting thing is that Twitter did that themselves by offering the poison pill solution.
Twitter is essentially committing suicide and screwing its shareholders just to try and block him from buying out the company and making it a free speech platform. Twitter is small among most other social media tech giants & dwindling in popularity, but it still largely drives the news cycle. The left knows this and is fighting tooth and nail to retain that.