Prior to T45's SCOTUS appointments the answer would have been a resounding, YES.

Now I'd say the odds are more like 5-4, NO.

I'm more cautiously optimistic.

Remember, this is a tactic that has more traditionally been used by Democrats than Republicans. As a very general matter, Presidents only have the power to do things if Congress has passed a statute telling them they can. So those who want an expansive federal government have long gone looking through the nooks and crannies of the U.S. Code, trying to find statutory "hooks" upon which they can hang the policies that they want to implement. You find an old statute with language broad enough to possibly support a strained interpretation....and then voila! You've got authority for your rule. That's what the Administration is doing here - dusting off an old statute from the back of the Code book (1798!), giving it a strained interpretation (unauthorized migrants are actually an invasion!), and hoping the courts let it slide.

But some of the recent SCOTUS decisions that Democrats have reviled actually pushed back on this exact practice. When SCOTUS struck down the Biden Administration's efforts on certain COVID workplace requirements and student loan forgiveness, they drew much more stringent lines around the Executive's ability to take old statutory language and use it in novel ways under generous agency interpretations to give the agency more power.

It's not always a winning bet to expect internal consistency from justices when faced with a different fact pattern - but I think that conservative judges genuinely don't like the idea that the Executive can just "find" some old statutory provision and claim a novel power that Congress probably never contemplated, just because the language is broad or vague. So I wouldn't be shocked if some of them don't want to go along with this idea.