Probably not. From this comment:

"They were under the tables and stuff and on their knees, but they had no chance."

I infer that the fatalities were in the group already in shelter, not the group in the woods. Had they had extra warning - and I've seen no reports of that there was an earlier radio warning - they wouldn't have gone anywhere else. They heard a tornado siren after sheltering but before the tornado struck.

It doesn't minimize the importance of having a cheap weather alert radio at such a camp, but it appears in this case it was not a contributing factor: the tornado directly struck and took out the shelter.