No, action surge can't be used while surprised in this context

Arcane Charge says:

At 15th level, you gain the ability to teleport up to 30 feet to an unoccupied space you can see when you use your Action Surge

To use an ability, you must do (and thus be able to do) whatever that ability is allowing you to do.

Action Surge says:

Starting at 2nd level, you can push yourself beyond your normal limits for a moment. On your turn, you can take one additional action.

So, using Action Surge requires you to take an action. If you aren't doing that you aren't using the ability at all. You can't just call out the name of an ability, not do anything that the ability says, and then claimed you have used it.

In 5e, there no such thing as an action declaration phase. You don't declare doing something before doing it. So doing it simply means doing the thing that the ability describes. Saying "I use Action Surge" is the same thing as saying "I do the thing that Action Surge says I do".

The Arcane Charge itself seems to support this interpretation:

You can teleport before or after the additional action.

Note how it does not list not taking the action at all as an option. This supports the argument that "using" Action Surge means using that additional action.

Since being surprised prevents you from taking any actions, you cannot take the action from Action Surge. Since you cannot use the action from Action Surge, you cannot use that ability. And since you cannot use the ability, you cannot benefit from Arcane Charge.