It depends on your cellphone, of course, but pictures from a good cellphone are quite alright in a show.
I've done several shows like this, mostly about my travels abroad, and I was pretty happy with them.
I wouldn't venture on weddings or celebrations , but all the rest are perfectly acceptable.
Try to shoot more horizontal pictures than vertical ones, so that you can fill the page in your show, and don't take vertical video clips. Those look awful on a wide screen, in my opinion.
In any case, people who are good with cameras, and know how to take pictures, are also good with their cellphones