Without a doubt. But what would Lee have thought if his subordinates had decided that they were no longer part of the US when they were risking their lives in Mexico or on the Texas frontier? When Lee was fighting in the Mexican War, did he really think of himself as a Virginian first and foremost with his actions to be determined by whether Virginia's government supported the war?
Winfield Scott, a Virginian who served in both the War of 1812 and the Mexican War, didn't think so. 2/5ths of the Virginians in the US Army in 1860 didn't think so either. The number similar if not higher among Southerners in the Navy and Marines. Many of them faced great enmity from their families and neighbors, but their choice did represent an honorable alternative to Lee's.
Many of Lee's relatives stayed with the US, rather than go with the secessionists. They wondered why someone who believed secession would mean "ruin and anarchy" as Lee did, would go along with the Confederacy. Was that really the wisest and best choice? Is it really something we aren't allowed to question and criticize?
Good reads on this point are the books “April 1865” and “Lincoln at Gettysburg” by Gary Wills.
Garry Wills had a very definite agenda in writing that book (and the rest of his books). He also loves to show off how smart he thinks he is. He's a very bright guy indeed, but he's not the most reliable commentator.
Certainly the Civil War changed America, but a major reason why it did was because many Americans already thought in national terms. That more didn't had a lot to do with the controversies over slavery and abolitionism.
You’re asking the wrong question.
The question is, had Virginia seceded rather than take part in the Mexican War, and the US President decided to invade to force the state back into the Union, would Lee have resigned and gone home?
I think the answer is yes.