Can you actually input morse faster than a keyboard?

No.

The world record in sending letters (random 5 letter groups) is 283 for one minute: http://www.hst2017.org/en/records

This is with a special key that's made for high speed telegraphy. Anything on a mobile device would most likely be a lot slower.

There are some sample sounds of similar speeds, which you may find interesting.

I don't know. I feel that speed is not important to me, it's the accuracy (gained with practise, of course) that I want. I make a lot of typos, it takes me much longer to edit something on a touch interface as my thumbs just don't seem to be very accurate. I guess you could say I'd rather slowly input the right thing the first time than to edit it quickly the second time