The aperture doesn't
necessarily have a theoretical effect on image quality, though it will certainly impact the depth of field, and will be shallower at higher focal lengths for the same f-stop. Also, in practice, due to impurities and imperfections in glass and other inefficiencies, there will be effects, though they can definitely be managed and are always trade-offs. Usually with aperture it's well worth it to increase the aperture.
What you'll find with professional glass lenses, with variable apertures, is that sometimes you do need to decrease the aperture (higher f-stop) to get the sharpest possible image from the lens. At wider apertures you're collecting more light, from closer to the edges of the glass, at higher refractory angles, travelling through more glass, and thus sharpness goes down. The other side of the aperture though, aside from DOF, is that it lets more light through, so you will also get more flexibility in general on trading off proper exposure time vs motion blur, which is great for low light handheld photography.
I would expect for mobile lenses, though, since they know it's a fixed aperture, they've done their best to mitigate those effects, aside from the fact that your DOF is definitely fixed since there's no variable aperture on your phone camera lens. Honestly the only way to know for sure is wait for somebody like DPReview to run the camera through their test suite and get some objective numbers/photos to see what, if any, impact there is from the wider aperture.
A DOF calculator can be a helpful resource to get a gut feel for the relationship between the various inputs that affect DOF. e.g. https://www.photopills.com/calculators/dof