No because the core audience for PS will want their HD console to be the main focus. Sony will likely play it safe and do just that, making it the VITA 2.0.
The reason Nintendo pulled it off is because it is still a step above the WiiU and they put pretty much all focus on the hybrid.
A PS Switch would be seen as a step back if they gave it full focus and they would catch backlash from the media.
Nintendo was realistically the only one of the big 3 that could pull it off with decent odds of success.