Fall planting of Yuccas
Just as Tim wrote, have I also planted Yucca plants in all months which had not have frozen soil. And The casualties are not more in the fall, than in other times of the growing season. The best time for transplanting in our climate, is in early April (if the soil isn't covered with snow and frozen solid).
I do not plant any seedlings into the ground before a rhizome is well developed (at least 2 years old). I would however think, that if we had higher temperatures here in the growing season, the seedling would grow a rhizome quite fast in the garden. The temperature in June-july is usually between 8-10C during the nights (very short nights) and 18-22 degrees Celsius during the daytime, and occasionally up to 25C or a little higher during "hot spells".
Since the "dead" base of your Yucca feels firm, I am sure, that it will grow a new or more rosettes from the rhizomes.