By rule, video replay can not be initiated during play--that is, off-ice officials can not interrupt play to begin a video review. If the call on the ice was no goal, and video replay overturns that call, all play after the time the goal was scored is nullified; the goal will be counted, time will be set to the time the goal was scored, and any other action that resulted in the stoppage initiating the replay is also null, including any subsequent goals (rule 83.6). The lone exception to this is a penalty. The penalty will be enforced regardless of the team, however the time of the penalty will revert to the time of the goal being scored (rule 93.5).

Officials have discretion to go back and review it or not unless the coach elects to challenge the play (case in point, Denver in the Frozen Four). A coach must indicate that the timeout is being taken to challenge the play at the time of the timeout. Also of interest, one of the emphasis points is that all elements of the play become reviewable once the review is initiated. The example from the rule book being that if you're challenging that the puck was hit with a high stick, but it was actually kicked in, it will still be disallowed.

Here's the full text of the review rules.

93.4 Video Replay Criteria - The following criteria are subject to the use of video replay. Items 1-11 may be reviewed through either referee discretion or by a coach's challenge. Items 12-14 include a description of when review is allowed. The full criteria is below: 1. A puck crossing the goal line. 2. A puck entering the net before the goal frame is dislodged. (See 83.5.) 3. A puck entering the net before or after expiration of time at the end of a period, a whistle, or referee’s determination that play has stopped. 4. A puck directed into the net by a hand or a distinct kicking motion. 5. A puck deflected into the net by an official. 6. To correctly identify individuals who participated in a fight or committed an infraction. 7. To establish the correct time on the clock, or to determine the correct location of a faceoff. 8. To determine if an attacking player prevented the goalkeeper from defending the goal in accordance with Rule 73. 9. To determine if a goal was scored as the direct result of a hand pass or high stick by an attacking player to a teammate or deflection off of the goalkeeper. 10. To determine if a goal was scored before a penalty infraction occurred. 11. To allow the on-ice officials to review infractions that may result in the ejection of a student-athlete. 12. To determine if a goal was scored as a result of an offside play or as the result of an undetected too many men on the ice infraction by the attacking team. The opportunity for review exists during the time the puck entered the attacking zone illegally as a result of the offside infraction and until the puck either: a) Leaves the offending team’s attacking zone; b) A stoppage of play occurs and a faceoff is conducted; or c) The defending team gains possession and control of the puck. During regular-season competition, a team must use its timeout except in last 10 minutes of the game or in the overtime period to have these plays reviewed. In postseason competition, offsides and too many players infractions are part of the criteria for review without a coach's challenge. 13. To determine if a goal was scored, as a direct result of the puck deflecting off of the protective netting above the glass, by the first team to gain possession of the deflected puck. A coach's challenge must be used to have this reviewed. 14. A puck directed or deflected into the net by a high stick. (See 83.6.) A coach's challenge must be used to have this reviewed. 93.5 Non-Detected Goal - In situations where a non-detected goal is awarded, officials will reset the game clock accordingly. If penalties occur prior to or after the undetected goal, these penalties will be enforced regardless of team. 93.6 Allowable Time for Review - Any potential goal requiring video review must be reviewed prior to or during the next stoppage of play. No goal may be awarded (or disallowed) as a result of video review once the puck has been dropped and play has resumed.