You can do this without any problems, but only in the rear shaft!

The User's Guide states the following regarding media types: Unsupported media types: Too thick paper (paper weighing more than 105 g /m2 (28 lb), except for genuine Canon paper).
However, I occasionally print on 120 g (non-Canon) paper using the normal paper feed on this printer and it works. However, I have never tried printing on 350 g paper or even thicker.

I just printed photo cardboard (Obi, Migros) with it through the rear tray. It worked without any problems. I don't know the exact weight, but it should be in that range.