[RPG] Does a fighter’s Action Surge allow 2 off-hand attacks as bonus actions?

You can wield & attack with two weapons without any special class feature or feat.

Like most contests, however, some restrictions may apply. From the PHB, p195 (emphasis mine):

Two-Weapon Fighting
When you take the Attack action and attack with a light melee weapon that you're holding in one hand, you can use a bonus action to attack with a different light melee weapon that you're holding in the other hand. You don't add your ability modifier to the damage of the bonus attack, unless that modifier is negative.

As long as both weapons are light weapons, you can attack with both at the cost of an action for the first attack, as normal, and then a bonus action for the second attack. The second attack does not receive your ability modifier as a bonus to damage the way attacks normally would.

Fighters & some other classes have an option for their Fighting Style class feature which is also called, confusingly, Two-Weapon Fighting. This feature is not required to attack with two weapons as described above; the benefit it gives is to allow you to add your ability modifier to the second attack's damage.

The Dual Wielder feat is likewise not required to attack with two weapons as described above; it instead provides additional benefits and removes other restrictions/penalties when you choose to do so.

Dual Wielder and the Two-Weapon Fighting style make you better at fighting with a weapon in each hand, but are not required to do so.

You could certainly Dash first to increase you movement allowance, then attack the first mook, then move, then attack the second mook. That's not exactly what you're asking about though, since you want to see the result of the first attack before deciding to Dash.

In the strict rules as written, however, only movement is explicitly allowed to be broken up arbitrarily. Taking the Attack action doesn't "add to your attack allowance" the way Dash adds to your movement allowance.

Implicitly, when you take an action, you are committed to completing the entire action unless you have a rule that says otherwise. "Moving Between Attacks" is one such rule, and object interaction (PH p.190) is another:

You can also interact with one object or feature of the environment for free, during either your move or your action.

By this reading, you have to complete all the Extra Attacks that are part of the initial Attack action before using Action Surge to Dash.