The regulator is going to be about the same voltage (say 4.95 volts) every time you start it up normally. The 2% is usually referring to unit to unit variation. So this you can calibrate out no problem with a single unit, at room temp, at a certain load current, etc. However, you will also notice a spec on better regulator data sheets for variability over conditions. This will be stated like "Max +/- 3% over Line, load and temp". So even though you calibrate at one point, if the regulator gets hotter or colder, if your line input voltage changes (like say an alkaline battery pack going from full to dead), or if you circuit changes it's current draw, your calibration will be useless. Basically you don't really want to use a regulator for a reference if you really care about accuracy. Find a cheap voltage reference (something like a 4.096V shunt reference should be cheap and accurate to 0.5% or 0.1% depending on product grade) and use that as the reference to your ADC or whatever circuitry needs the accurate reference.
So yeah, I would really suggest a precision reference. They will get you to 0.5% cheaply and even better if you can spend a little more.