When we bottle beer is is ideally in a condition called "Cask Bright" that's just the technical term for really clear. To give you an example I do a fair bit of my brewing in glass demijohns (25 L bottles). When the beer is ready to bottle I can lick my finger stick it on the bottle and see my finger print right through the beer (call it about 300 mm).
At this time the beer still has about 10,000 yeast cells/mL, 25,000 mL makes for 2,500,000,00 yeast cell that's 2.5 Billion cells.
That's a lot less than most people have when they bottle so you can think of that as a minimum yeast loading.
Normally when you bottle the beer and add some more food, the yeast metabolises the priming sugar making CO2 and some more alcohol, then goes and lies on the bottom.
The amount of yeast I've mentioned isn't going to make a slab but rather a very fine dusting of yeast.
If you haven't removed all the yeast from the beer (i.e. filtered sterile) no matter how you add the priming sugar that same yeast is still there and will eventually sediment out in the bottle
What you have proposed won't change that one iota. Nor will any device that lets the sugar mix into the beer.
If you have sterile (yeast free) beer and then introduced a device that contained both the sugar and the yeast then it might be possible that some sort of membrane that will keep in the yeast and allow the CO2 that is evolved migrate out and dissolve in the beer might work. The dialysis tubing mention above has real possibilities. But first you need sterile beer.
Second you need a membrane that will let the CO2 out, I did a bit of a search and one of the most permeable membranes tested was a "Rubber Dental Dam" having a glance at wiki maybe a condom isn't such a bad idea mind you I don't think a lubricated one would be a good notion and "Hay mate want a beer ... just wait until I get the franger out" might not be a great party starter.
MHB