I see no reason delegates could not meet in Montgomery to discuss political affairs.
The states that already seceded (in January 1861) sent delegates to the Convention. These states, including South Carolina, Mississippi, Florida, Alabama, Georgia, and Louisiana were effectively independent, sovereign states.
Virginia, Arkansas, North Carolina, Tennessee, Missouri, and Kentucky were not represented at the Convention, along with other Northern states still in the Union.
The only northern states invited to the Montgomery convention were Delaware and Maryland (technically south of the Mason-Dixon line).
They didn't go there to merely discuss political affairs, but rather to convene a constitutional convention. Convening a constitutional convention to change your form of government and excluding your political enemies is not very good form. In fact, they didn't follow the forms prescribed for such conventions listed in the U.S. Constitution, so it wasn't done legally.
The only ways open to the south to secede legally was either to get an amendment to the constitution, or by a constitutional convention. There is no way an amendment would have passed. The only way a constitutional convention would have worked is by contravening the constitutional rights of northern states.