The T200 is designed to run best at 16V, and is rated to run well up to 20V. Beyond that, long term performance and durability has not been tested, though I can say at 27-28V there is imminent danger of overheating and burning out the thruster in minutes or less. Running beyond 20V will increase wear and significantly reduce efficiency, there will be some boost in thrust but most of the additional power will be wasted as heat. However, independent of the 26V rating of the Basic ESC, it has an approximately 30A constant current rating, depending on cooling. At 20V, the T200 draws about 30A constant, near the limit of the Basic ESCs capabilities. If you wish to run a T200 at beyond 20V at full throttle, you will need to use a different ESC with a higher current rating. If you limit thruster power to 600-650W or so by attenuating the throttle, it can be possible to use the Basic ESC and T200 at beyond 20V.
Running beyond the rated voltage of our thrusters does not instantly destroy them, but the rapidly diminishing returns in performance, increased wear, and drop in efficiency mean that we do not recommend doing this. The bottom line is the T200 is rated to run at 6-20V, and exceeding this against our recommendation can have mixed results, as well as void the warranty.
If you are planning on increasing your battery voltage, you need to check the documentation of every other component you have hooked up to make sure they can handle the higher voltage.