Nope.
Wrong. The current state seal was adopted in 1914, it modified the prior state seal which was merely a beam with three pillars, along with 4 banners. The Georgie arch was built in 1856.
Prior to 1914, the actual state seal was not an arch, although it was called that. It was a beam supported by three pillars, each with a banner, and each banner stating one of the three words that make up the state motto. The phrase "constitution" appeared above the arch, but the statute stated that this was the same as the banners stating "wisdom," justice, and moderation, except that the constitution banner was described as a golden banner, above the foundation supplied by wisdom, justice, and moderation. In 1914 the statute changed and stated that the "constitution" was part of the structure, adding an arch to something that was not an arch. This is clear because in 1914 instead of there being 4 banners as part of the state seal there were only three.
In short, it only became an arch in 1914. Long after Georgie built its arch. That said, the symbol has always been referred to as an arch, even though the statutory text did not describe it as an arch. This simply means that not only did Georgie not understand what an arch was, but that they couldn't read, either.