Especially if you're departing from SIN, yes you may upgrade to J ....
But the price will simply be the full fare difference between what you paid for your ticket and the full J fare from SIN to NRT which can be anywhere around US$ 3000 oneway !
If you can upgrade your ticket for less before you travel on a lower J class fare, do it. Cos you'll be whacked with the full Business class fare at the airport.
SQ does not need to sell you a seat for cheap. They'll sell it you at full fare.