I've led a food/art/culture study abroad program in Italy, and from a food and culture point of view, requesting white sugar is well within the norm for cappuccino; it is served virtually everywhere cappuccino is served in Italy. However cappuccino is often served as a tourist expectation, rather than a typical Italian beverage, and when Italians DO have cappuccino, it's rarely after noon. More typical is the simple caffè that Americans would call an espresso or demitasse.
For politeness' sake, here are some considerations regarding white sugar:
If your cappuccino is served with a rock sugar stir stick, you should use that instead of asking for white sugar separately; rock sugar IS white sugar, crystallized, and they've gone to some effort and expense to provide it in that form.
In polite company, especially in Italy, don't dump piles of sugar into your beverage or food. Though the phrase "one lump or two" is largely forgotten these days, dumping 6 teaspoons into a cappuccino labels you as an American boor on your way to diabetes. Traditional Italians believe in moderation in things such as sugar and alcohol consumption.
It IS considered impolite to add sugar to a number of drinks where it would be considered an adulterant, including Japanese green tea, wine, beer, etc.
It is also considered impolite to add sugar to soda because it will often cause a fast rising foam that will spill over onto the table.