No the PO shouldn't be drawing designs and really you don't want them to.

For example, lets say im the CEO and I want a website to sell the company's widgets god dam it!! It's a small company so I am the PO on the project. There are two ways I can go

1. Specify only high level business requirements and let the experts fill in the details

  - Requirement A. This site Has. To. Sell. Widgets!
  - Requirement B. You can only have £100 per annum for hosting!

2. Specify exactly what I think will make a good site for selling widgets

  - Requirement A. part 1 section iii : The site must have the company logo in gif format with animated flames. it must fill the users entire screen
  - etc ...

With method one I trust the marketing and UI guys to come up with amazing flaming gif ideas that are proven to sell the most widgets

With method two I don't really need the marketing and UI guys. Any fule kno flaming gifs are the best and the devs will make it exactly to my specifications while charging me a daily rate.