The law says no...........
[LAWS]5.7 Other time regulations
(a)
In international matches, play always lasts eighty minutes plus lost time.
(b)
In non-international matches a Union may decide the length of a match.
(c)
If the Union does not decide, the teams agree on the length of a match. If they cannot agree, the referee decides.
(d)
The referee has the power to end the match at any time, if the referee believes that play should not continue because it would be dangerous.
(e)
If time expires and the ball is not dead, or an awarded scrum or lineout has not been completed, the referee allows play to continue until the next time that the ball becomes dead. The ball becomes dead when the referee would have awarded a scrum, lineout, an option to the non-infringing team, drop out or after a conversion or successful penalty kick at goal. If a scrum has to be reset, the scrum has not been completed. If time expires and a mark, free kick or penalty kick is then awarded, the referee allows play to continue.
(f)
If time expires after a try has been scored the referee allows time for the conversion kick to be taken.
(g)
When weather conditions are exceptionally hot and/or humid, the referee, at his discretion, will be permitted to allow one water break in each half. This water break should be no longer than one minute. Time lost should be added on at the end of each half. The water break should normally be taken after a score or when the ball is out of play near the half way line[/LAWS]
I guess you are saying the game ends under (e) because the next step is a scrum.
but could you argue that the Law refers to 'awarding' a scrum, which implies there has been an infingement, resulting from which the referee awards a scrum.
in this scenario a there was no infringment, the scrum is just a way to restart.
A similar scenario would be if time expired and the referee slips on his face and gets mud in his eye. the ref would have to blow the whistle - would that end the game ? it would be a bit unfair on the players.