Hi, Annie. The weather seems to vary so much from year to year. But I think the last week of April could still be snowy. I know Joe Flavin walked in April (earlier I think) and got hammered. I think Reb went in late April once and was in snow up to her hips, but maybe I'm misremembering. You could pm them. One possibility would be to start from Leon and when you get to Pola de Gordon find out what the conditions are. And then hop a bus to Oviedo if you have to -- since it's right on the Camino and the bus route.
The lead-up to the mountains continues up till about 5 (maybe 8) km after Pola de Gordon, in Buiza. From Leon to that point, there are some ups and downs but nothing serious. The ascents begin in Buiza, but they are not extreme ascents. They are breathtaking ascents, but you will lose your breath from the beauty not from any extreme elevation gains.
Will you be walking into Leon? If not, my idea about walking to Pola de Gordon may not be very helpful. Buen camino, Laurie