The Secret Service would also protect the President from arrest. Such action would simply not be allowed.
The best outcome is if Trump attempts to enter, but finds his path blocked.
That would be an unlawful act on the part of the Secret Service. They cannot usurp the powers of the House. Their role is not to subvert the Constitution nor law, but to protect the President from physical harm and that's it. Naturally, they could escort the President to jail and safeguard him, but the moment they exceed their mandate by usurping the powers of Congress they become criminals under US law if they interfere with non violent arrest.
This is the specific charge to the Secret Service under 18 U.S. Code § 3056
"The President, the Vice President (or other officer next in the order of succession to the
Office of President), the President-elect, and the Vice President-elect."
That's it. There's no protection from lawful arrest- at all. Again they would naturally protect Trump from physical harm. To do that they can restrain the President from harming himself and escort him to jail where they can provide security, delivering the jail mandated food themselves, even watch over its preparation.
But the Secret Service is not one of the Shah or Saddam. They protect, not serve him and above all else is the protection of the Constitution, even above Trump's comfort.