Most failures present themselves 10-30 days after grafting. I've had scions hold on for several months, only to then fail. It's impossible to be completely sure of success or failure based on any timeframe.
Watching the skin of the scion will be your best indicator. If it starts to shrivel/wrinkle, it's failing. If the scion loses its original green color, it's going to fail. If you receive scions covered in sooty mold, it can be hard to see the color changes. I never do it, but I'm sure you can clean the mold off with a little alcohol & water mix and some light brushing with a paper towel; you just need to see the color at the union and some points along the length of the scion, don't risk cleaning any actively budding areas or the head of the scion.
If you use buddy tape or stretch your parafilm as thin as possible, you can usually see the color well enough to see signs of a failure early-on. If the head of the scion starts turning black, it's nearly always a goner. If either side of the graft at the union starts to turn yellow/brownish in color, it's also a bad sign. If it turns dark-brown/black, it's a real bad sign. It's important to look at all sides of the scion at the union, one side can fail while the other has a good connection; any connection at all can still be a success.
I use buddy tape, a clear plastic wrap and clothes pins; these make it easier to check the union without having to rewrap (which comes with it's own perils). If you catch a failure early, you can usually reattempt and might have success. Just be sure to cut it back until you don't see any brown discoloration in the flesh of the scion.