No, see: https://news.ycombinator.com/item?id=49973037
There's nothing illegal unless someone seriously thinks Obama signed it. The easiest example would be his signature on his wikipedia page. Clearly he didn't sign that page, nor (probably) did he authorize it.
I don't understand your argument. Wikipedia and a satirical cartoon are both things clearly not made by Obama, nobody in their right mind would be "fooled" by the presence of his signature.
These cartoons are intentionally drawn in the style of a cartoonist and feature their signature. The goal is forgery. The whole point of these AI-generated images is to look like the real thing.