No.
Shenmue III as a game and title makes perfect sense. Shenmue is a sequential series that needed a third game to continue the series. Meanwhile, Sonic has had games before and after Adventure 2 that continued the story and the series. Sonic 4's intent was to continue the 2D gameplay which really had been missing from home consoles since Sonic 3 & Knuckles. But 3D Sonic, which the Adventure series represents, had continued on since SA2 with several titles. Some very different, some very similar to the Adventure formula.
If a Sonic Adventure 3 was made in the near future, what would be the point of the title? We have already seen games continue the storyline of SA2 (Heroes, Shadow), we have already seen games continue the gameplay style (Unleashed, 06), and since Unleashed SEGA has given the Sonic series a light reboot where storyline between games isn't as big a deal and games themselves have adopted some elements of the Adventure series and some new elements.
Basically, I don't really see a point.