Yes—many Tamron EF lenses can work on Canon EOS R bodies via the Canon EF-EOS R adapter, but compatibility depends on the exact lens model and firmware.

From user reports here, some Tamron EF lenses on an EOS RP worked fine for aperture control, stabilization, and autofocus when updated to the latest firmware. However, one report says a Tamron SP 70-200mm f/2.8 G2 did not work on an R5 even with current firmware.

A second point raised is autofocus behavior: when focus is not immediately acquired, some Tamron telephotos may scan very slowly through the focus range. In normal use this may not matter much, because autofocus often jumps close to the correct distance and locks quickly, but in difficult focus situations it can be frustrating.

So the safe conclusion is: adapted third-party EF lenses can work well on EOS R cameras, but you should verify support for your exact Tamron model—especially the 70-200mm version you own—and make sure firmware is current before relying on it for paid or critical work.