No for several reasons. The first is that the Shawnee were the most mobile people in North America at the time. They ranged as far north as Canada and as far south as Florida and as far West as the Mississippi and the Great Lakes. This mobility made them the traders and diplomats par excellence of indigenous North America, and Shawnee was tantamount to a lingua franca in almost all Native communities east of the Mississippi. There is no good way to represent that kind of mobility in a Civ game, at least not yet. IMO this is even a bigger issue for the Shawnee than it is for, say, the Scythians or Mongols.
The second is that Tecumseh has become an icon of Manifest Destiny: the great Noble Savage whose brave resistance to American imperialism proved the futility of resisting America's inevitable destiny to spread from sea to sea. There's a reason he's the most famous Native American, and it's only partially a result of sincere respect for the man.
The third is that Tenskwatawa is often overlooked but was as essential to the formation of Tecumseh's confederacy. While woefully incompetent when actually left in charge, he was charismatic, and his religious visions were essential to Tecumseh's movement. Historians argue whether Tecumseh was a sincere convert or a pragmatic operator, but that's not really relevant to the massive influence Tenskwatawa's religious movement had. I recommend R. David Edmunds's
The Shawnee Prophet if you want to learn more.
If you want someone who fills the role of a visionary Native American leader who championed pan-Indian unity without becoming a romantic icon of American expansionism, I'd recommend Joseph Brant (Thayendanegea) in his stead.
He was often portrayed to wear Redcoat officier / General unifrm. I'm not sure if he bought from Brits or the Britsh Government gifted him with it so to sting the fledging US of A (containing westward expansion) at the very early years of 19th Century? (One of many many Casus Beli of War of 1812 between the USA and British Empire, i'm not sure when or where did Americans found incriminating evidence of British sponsorizations of Shawnee warpaths or did Wayne's Legion discovered some clues linked Tecumseh with British Empire or is there any reports that American troops had 'captured British persons found amongs Shawnee' ?
Prior to the War of 1812, the relationship between Tecumseh and the British was...complicated. They spoke words of encouragement and gave limited material support, but at the same time they didn't want to alienate the Americans prematurely. Tecumseh was very frustrated by their professions of friendship that were rarely backed up by actions. At the same time, however, Tecumseh was not a rabid warmonger. He tried very earnestly to find a peaceful solution with the American settlers. NB the officials in Washington generally
also wanted to find a peaceful solution--but territorial governor William Henry Harrison (yes, the future president) was more interested in his own political career and actively antagonized Tecumseh and the Shawnee, figuring an Indian war would look good for his career. A great deal of the tragedies between the Shawnee and Americans are squarely Harrison's fault.
Tecumseh and his supporters moved to Canada during the War of 1812, and Tecumseh was given a formal commission by the British. Without question he was the most talented general on either side of the Northern theater, and he also worked hard to make sure atrocities weren't committed against prisoners by his frustrated followers. Ultimately, he wasn't given the support he needed by the British, and he died in battle. The War of 1812 was an embarrassment for everyone involved, horribly mismanaged by both sides, and of no real lasting consequence except in launching a few political careers.
When I've tried to create a Shawnee civ idea, I gave them Red Sticks, which are technically Muskogee, but were strongly allied to Tecumseh and acted as his enforcers.
To be fair, the Red Stick Rebellion was coming with or without Tecumseh. Tecumseh did have supporters among the Chickasaw, Cherokee, and Creek (he was raised among Chickamauga Cherokee for a time and his mother
may have been Chickasaw), but he was never actively leading them--more spurring them to act on behalf of the British. Pushmataha had
stern words for Tecumseh's attempts to recruit among the Choctaw.