So the sky isn't really falling.......
[Continues to run in circles screaming]
No, it's still bad.
Well, technically, the feds could use a treaty ratified by 2/3 of the Senate to force gun control laws to the state level if they were deemed Constitutional. This might be pertinent in the unlikely event that the Supreme Court rules that the feds have no authority under the Constitution to force gun control regulations onto the States. So it can be used a jurisdiction hack to get around state's rights, but not as a hack to bypass the Constitution. Sorta. You can more or less ignore that part, because it's a technical legal hack thing that'd only interest lawyers.
The other bad part is that the feds are granted near unlimited authority over the borders. Many Constitutional protections do not apply there. Most don't, actually. Everything from the 2A to free speech to search and seizure to many other things. So they could use a treaty to ram through restrictions on importing or exporting of some or all firearms, accessories, munitions, et al and be entirely Constitutionally in the right. That would be severely damaging. Imagine no surplus or imported firearms (or ammo), and domestic firearms companies losing all foreign sales.
Might want to run that by Ned or BW, though. IANAL.