Could I omit the raw sugar in this recipe (and add no substitutes), or would that be a disaster? My family doesn't have much of a sweet tooth so I...

The best ways to reduce sweetness in pecan pie are these:
1. Use an unsugared crust. I have one brisee/pie dough I use for *all* pies, sweet and savory, to do just this.
2. Use a mixture of sugars in pecan pie filling. Some sugars are less sweet than others. I don't want my pecan pie to taste solely of molasses so I use Lyle's Golden Syrup, maple syrup, honey, cane syrup (like Steen's).
3. Pecan pie is a custard of sugar, butter and eggs. A certain amount of eggs "sets" (aka coagulates) a certain amount of liquid. If you omit a percentage of sugar, you have to adjust eggs and butter accordingly.
4. Toast all pecans entering or topping pie. This flavor will offset the sugary sweetness.
5. Use non-iodized sea or kosher salt, and add a pinch more than you think necessary. Very sweet baked goods benefit from a counterbalance of salt. If you're not squeamish about raw eggs-- taste custard before you put pie in the oven. Most people think changes cannot be made along the way, but they can.
6. Use only real vanilla extract, and stay away from Tahitian. Madagascar vanilla extract is the best flavor for these ingredients.
7. Cut slices of pie small-- it is a very rich and sweet dessert, and it will be a balanced last course if they have a few bites, not 10. Pair with unsweetened whipped cream. If I'm in the mood, I'll add a slash of cognac to the cream as it's whipping-- its flavor complements all the other warm flavors.
T

Another tack would be to balance the pie with a beverage that's on the bitter side, the classic solution being coffee.

Hilarybee is correct: the balance of the recipe would be upset, and the pie wouldn't set. FWIW, Pecan Pie is a VERY sweet dessert. If you family does not go for "very sweet," you are better off to choose a completely different dessert. Apple Pie, for example, you can use reduced amounts of sugar with no degradation to the finished product.

To clarify-- I wouldn't omit it and yes, I do think that would be a bit of a disaster. If your family doesn't like sweets, choose a dessert that requires less sugar. Like something with fruit that is already sweet.

Yes, I think that would result in a very runny/liquidy filling. The sugar is essential to creating the pecan pie filling and I doubt that the filling would set up without it.