Would a Dwarf's +2 to constitution be added to their ability stat, or just their modifier when making a roll?
It's added to the ability stat.
If you are using point buy then any racial bonuses are added at the end. If you are rolling then you add the bonus after assigning each roll to a particular ability.
This would typically provide a +1 bonus to CON based rolls.
It is added to the base score during character creation, after initial ability scores are decided (Or race change with Reincarnation or something). It is an untyped, inherent increase, not a bonus. It is treated as if the ability score started that high during ability score determination and it should not be written on the character sheet as a bonus.
If you have 14 CON and choose to be Dwarf, your CON is now naturally 16, not 14+2 bonus.
Ability modifiers in general, and racial ones in particular, affect your ability score, not just rolls that depend on it. So for stats like Con and Str, where individual ranks matter for derived stats, you would benefit from an increase to those derived stats in addition to the bonus on rolls.