By the time of the invention of the dynamite in the 19th century, the great wall had being irrelevant for a long time already. Intended to defend against northern nomads, it lost its use after 1644 when a Ming Chinese general allowed Manchu forces past the wall. The Manchus conquered China and established the Qing dynasty, which included Mongolia and Manchuria within its empire, thus removing the strategic threat that the great wall was meant to counter.

Short Answer: no. The Great Wall outlived its usefulness, which was never that great to begin with, about two centuries before dynamite was invented. The game mechanics are symbolism and game-balance issues.

The Great Wall that exists today was built during the Ming Dynasty, beginning with the fortification of some passes in the northeast near Beijing in 1373. It's better to think of the Great Wall not so much as one continuous fortification but rather as a series of connected garrisons: an undefended section of the wall did little to stop Altan Khan from raiding Beijing in the 1550, but in 1554 a beefed-up Chinese presence was able to stop a similar raid in the same spot. Previously, in 1449, a fortified guard station on the border was not able to prevent a 50,000-strong Chinese army from being annihilated and the Emperor(!) being captured by Essen Khan and the Oirat Mongols.

The Manchus were able to breach the part of the wall around the Liaodong and incorporate it into their state a couple of decades before they conquered the rest of China. They had a difficult time forcing the Shanhaiguan pass and taking Beijing by force, but were let through by the commanding general Wu Sangui. The Ming Dynasty was in the process of collapsing, and rebels led by Li Zicheng had taken the capital. Wu decided to throw his lot in with the Manchu Qing rather than the rebels, and pledged allegiance to them in return for rule over a large part of southwest China.

For Ming China, the Great Wall was only one tool in the box when dealing with the Mongols. Chengzu, the Yongle Emperor, led military campaigns into Mongolia five times in the early 1400 to break up threatening coalitions. The Ming also tried to ply the Mongol groups with trade, land, and titles, and liked to play the various factions and regional groupings off one another. Ultimately, the best tool in the toolkit was bribery (or giving in to extortion, depending on your point of view): as long as the Chinese gave enough gifts and allowed enough trade, they could forgo having to go to war, and everyone wins.

After 1644, the Chinese lands south of the Great Wall were politically joined with the Manchu and Mongol lands north of the Wall, and the Great Wall served no defensive purpose. The only Qing Dynasty wall I can think of is the Willow Palisade, and that was an internal boundary-marker separating the Manchu homelands from Han China; Han settlers were not to be allowed past it.

Dynamite was invented in 1867.

It should be noted that the last time the Great Wall served any military function was actually in 1933 during the beginning of the Second-Sino Japanese War. The First Battle of Heibei (also known as the Battle of the Great Wall) saw underarmed Chinese forces garrisoning sections of the Great Wall in an unsuccessful attempt to fend off the Japanese offensive