"Maybe, maybe not. I don't know.", as we used to say.
Here's the problem. Abbott and the other governors have directly defied the orders of the Feds because TX wants to follow the US law while the Feds want to break US law. Anyone who is thinking knows that Biden & Co will brand them as traitors and go after them far harder than they went after Trump. Also, if some elements of the NG refuse to be federalized and side with TX, they will be court martialed for failure to obey a lawful order and possibly treason. For those very reasons, Abbott and his supporters, including those in the NG, might feel that their best option is to push through this, no matter what the consequences. Also, unlike 1960-1990, the NG does have a reasonable amount of advanced training and combat experience. Some units may even have more than their active duty counterparts, depending on the branch.
If Biden backs down, he and the Feds may be viewed as weak so they feel that they can't afford to back down. We've gotten to the point that no matter how this goes, it doesn't end well.