They can do this. Remember, ATF declared flash powder to be a high explosive, which it is not, and KNO3-sugar rocket fuel to be an explosive, which it is not. Tomatoes are vegetables by Supreme Court order.
So they can “declare” NRA to be a terrorist organization, which would have o be straightened out in court, if you can find a lawyer willing to defend a declared terror organization in court pro-bono.
Speaking of the ATF, and terrorist organizations, the ATF is state-sponsored, and, through operation Fast and Furious, knowingly caused firearms to be sold to known straw purchasers (a crime) and then knowingly let them walk across the Mexican border (another crime ... unlawful export) and then used the uptick in violence, on both sides of the border, and including the murder of a US federal agent, together with the trace information they themselves did, showing the guns were purchased in the US, to press for stricter laws against guns and gun dealers. But wait! The definition of terrorism is “using violence or intimidation for political purposes.” This is precisely what the ATF was doing with Operation F&F. And they violated multiple laws in pursuing their goals. Including being accomplices in murder of a US federal agent. That’s terrorism, folks! And unlike the NRA, which is just a figurehead, and hasn’t been directly tied to any of the recent mass shootings, the ATF was directly involved in both the unlawful gun sales and in the use of the resulting violence to publicly lobby for changes in gun laws.