I think this is possible, but it would be highly impractical. The best option is to drive, or take a greyhound bus which costs about $80.
The driving distance from Kelowna, BC to Edmonton, Alberta is 555 road miles.
Edmonton, AB, Canada to Kelowna, BC, Canada, will take about 11 hours 20 minutes to drive the 893 km. (555 miles).
125.00
894 km
Take Yellowhead west and stay on it till you see the sign that says to turn of to go to Kelowna
It is 556 miles according to Google Maps.
It's about ten and a half hours.
890 km
About ten and a half hours driving.
The flight distance for direct flights (if available) is 360 miles.
from edmonton alberta to valemount bc
Trans-Canada Hwy and Queen Elizabeth II/AB-2 N.