Uh, no. Sign languages, like American Sign Language, are not "simplistic" versions of spoken languages. They are complete, complex languages with their own robust syntax and grammatical structures. A better way to explain this is that it's like an adult who is natively fluent in one language trying to read subtitles in a second language with which they don't have working fluency and rarely, if ever, speak.
To expand on this, it's commonly believed that sign languages are simplified versions of the local spoken language. Indeed, it wasn't until ~1960[0] that these languages were seriously studied as "real" languages.
At least part of the reason a Deaf person might have poor grammar in a spoken language is because said spoken language is almost always at least their second language.
Sign language is more like watching a movie than listening to radio. It's extremely spatial, with space around the body used to indicate grammatical elements and their relation to each other.
Spoken languages are far more similar to each other than to sign languages.
Subtitles are like watching a movie with the green screen instead of the scenery filled in.
Source: My degree in American Sign Language.