Sometimes, but compatibility is not guaranteed.

From user reports, the Canon Extender EF 2x III does physically mount and autofocus with at least the Sigma 70-200mm f/2.8 OS on Canon APS-C bodies like the 70D/T5i. However, Canon teleconverters are designed around specific supported lenses, so with third-party lenses you may run into three separate issues:

1. Physical fit: it may mount, but not every lens is guaranteed to clear the extender’s protruding front element and rubber light baffle.
2. Electronic operation: AF and aperture reporting may work, but full compatibility isn’t assured because the extender’s electronics are optimized for Canon-supported lenses.
3. Image quality: even when it fits and functions, sharpness, contrast, and aberrations can worsen significantly. Teleconverters often perform best on lenses specifically designed to work with them.

So the short answer is: it may work on some Sigma or Tamron EF-mount lenses, but you should treat it as lens-by-lens compatibility rather than assume universal support. Test the exact lens/extender combination if possible, especially if image quality is important.