Is using 2" roofing nails on the nailing fins of new construction windows enough to hold them in place permanently? It seems to me like there should be some fasteners in the extension jambs, but maybe I'm just remembering back to when I installed some replacement windows (without nailing fins).
Matthew PK offers some very specific instructions. I happen to disagree with most of them, but they may work for some windows. I will simply state that every new window comes with specific installation instructions. You should follow them. Otherwise you will void the manufacturer's warranty.
Here is an informative article from Fine Homebuilding:
As far as fastening the jamb extensions to the trimmer stud goes - unless the window installation instructions specifically forbid it you may want to shim and trim screw just to guarantee plumb/square. The casing is typically what connects the jamb extension to the trimmer studs.
You should apply silicone in a thick bead under the flange, including under each fastener penetration. Some people choose not to apply silicone to the bottom lip of the flange.
You should screw through every other flange hole. Wipe silicone over the top of the fastener.
Finally, once the silicone is dry, you should apply flashing tape to the sides, then the top of the window. Some people choose to flash the framed opening as well, before mounting the window.
So, to answer your question: no, simply nailing the fins is insufficient.
Using silicone behind a vinyl window flange (flanges constructed as part of the window frame, not tapped on) will not only void most warranties but also have the potential to break the window in temperature changes. Vinyl expands and contracts in hot and cold weather. This is why many high quality siding panels have a thermometer taped onto each panel with the appropriate position to nail. This is why Azek vinyl decking seams will look perfectly tight in one temperature and open up in another, only to find their way back to the tightened position the next morning. This is also why many window flange nail holes are oblong shaped and not circular, to allow room for expansion. Waterproofing comes from the outside prep not hidden under it.