No, Saving Throws are not an ability or skill check.
Although you add your Dexterity modifier to the Reflex saving throw, it is its own mechanic separate from a standard Dexterity ability check or Dexterity-based skill check like Acrobatics.
These saves test your ability to dodge area attacks and unexpected situations. Apply your Dexterity modifier to your Reflex saving throws.
Note that the wording simply says "Apply your Dexterity modifier"; if it said "Make a Dexterity check", it would have been subject to the armour check penalty.
Further evidence that they're separate courtesy of @Sdjz:
You apply your character’s Dexterity modifier to:
- Ranged attack rolls, including those for attacks made with bows, crossbows, throwing axes, and many ranged spell attacks like scorching ray or searing light.
- Armor Class (AC), provided that the character can react to the attack.
- Reflex saving throws, for avoiding fireballs and other attacks that you can escape by moving quickly.
- Acrobatics, Disable Device, Escape Artist, Fly, Ride, Sleight of Hand, and Stealth checks.
As you can see, the skill checks you roll against Dexterity are listed separately from the saving throw point, indicating that they are not the same thing.
There is also:
Ability Damage: Damage to your Dexterity score causes you to take penalties on Dexterity-based skill checks, ranged attack rolls, initiative checks, and Reflex saving throws.