Unless I'm mistaken, he can buy general admission any time. I don't think Belmont sells out general admission or clubhouse, since you're not guaranteed a seat. It's going to be bedlam, but it can be done. I'm going to buy general admission at the gate (earlier in the day), and while Smarty Jones' Belmont was crazy on general admission, I lived to tell the tale.
He might (might) be able to buy tickets for a reserved seat when he gets there- I had an acquaintance who bought two tickets for $75 each for reserved seats in 2004 from a guy outside the gate. But there's always the risk they're fakes.
Here's the link to the page about tickets on the NYRA site. It says walkup tickets will be available:
http://www.nyra.com/belmont/grandsta...elmont-stakes/