No, don't think it's possible, as the linked files will update to show the last saved state of the master file.
least of all because the linked files are nested in smart objects so if the file does change it won't show up until you open up the mart object first
Chuck is likely to be right - he usually is, but please tell me what I'm missing here from your process:
An AI document with three artboards :
A PSD with each of those artboards, placed in it as a linked smart object using "Place Linked"
I update the AI file - changing the colour of the square on artboard 1 and adding text on artboard 2
On saving the AI document the smart objects in the PSD in Photoshop are updated
Like I say - it is probably me missing the point
I had this same experience, instead of using multiple artboards, saving, and updating the Smart Object I just made all my artboards individual layers in the AI file and turned them on and off as needed. When I hit save it updated and worked fine. i haven't tested it recently, but in the past it worked fine through the layers function.
That's close but it's more like this
AI file with artboards
PSD file with artboards
Smart object with the linked file
now this was done so I could add effects and layers and what have you to each individual element. But that won't work as it is nested and PS won't update the nested files without actually going into them. Also if you do go into the smart object if it has been translated to fit the bg it resets to it's original size.
Thanks Josh - got it now. It was the linked smart objects inside the document smart objects I had missed.
If the only reason you nested the smart objects was to be able to use the distort and perspective transform controls and add different shadows then you could do this, which uses Perspective Warp instead of transform. That allows you do build your renders without nested SOs
Place linked each object onto the first artboard
Duplicate onto the other artboards
Use Perspective Warp instead of transform - this will allow you to keep the linked objects without nesting
Add drop shadows etc as required.
The links will be updated from AI
Update objects in AI and the Photoshop document changes :