Illegal Immigration?

This morning I saw an unintentionally ironic bumper sticker: "Remember the Alamo! Stop illegal immigration!"

Mexico welcomed American immigrants into its province of Texas, and offered them land grants, so long as they swore allegiance to Mexico and converted to the Catholic faith.

The Americans, who later led a war of secession and used a Catholic church as a fort (the Alamo), had no intention of doing either, and so swore a false oath. Did that make them illegal immigrants?