Having looked more closely at the initiative rules, I came to a different conclusion...
No, you wouldn't be able to use it
The Rules Compendium contains a list of steps which occur at the start of a combat (which are the same as those in the Player's Handbook):
1. Determine surprise. The DM determines whether any combatants are surprised. If any combatants notice enemy combatants without being noticed in return, the aware combatants gain a surprise round.
3. Roll initiative. Everyone involved in a combat encounter rolls initiative, determining the order of combatants' turns. You roll initiative only at the beginning of a combat encounter.
4. Take surprise round actions. If any combatants gained a surprise round, they act in initiative order, each one taking a single action. (Surprised combatants take no actions during the surprise round.) The surprise round then ends, and the first regular round of combat begins.
Rules Compendium pg. 189-190, Player's Handbook pg. 266
An initial reading makes it sound as though the action limitation only takes place during the surprise round, which happens after initiative is rolled. However, "Surprised" is a defined condition.
- The creature can't take actions.
- The creature grants combat advantage.
- The creature can't flank.
Rules Compendium pg. 234, Player's Handbook pg. 277
Considering Surprised is an actual condition, this means the line in step 4 about not being able to act during a surprise round is a reminder of the rule from the condition, rather than the rule itself. Since determining whether or not a creature is Surprised is the first thing that occurs at the start of a combat, this seems to imply that you can't use any powers that are triggered by initiative being rolled if they require an action.