Yes stamina is important. The effect of stamina could certainly be seen in the 4th quarter. If a player has a horrible stamina, his performance will be poor especially in the 4th quarter, whereas if a player has goos stamina, his performance in the 4th quarter won't be effected much.
Also, having better stamina means a player could play more minutes. So if your starting player has a good stamina, he could play more minutes on the court. On the other hand, if your backup has a good stamina but your starter does not, your backup is likely to receive some more minutes (eg...backup could play as much as 20 minutes).
I try to make sure that most of my players have at least mediocre stamina. I think stamina is pretty important in this game and I'd certainly avoid playing players who have horrible stamina as starters.