The Redmond Cycling Club routes the http://www.redmondcyclingclub.org/S2S/S2S.html Seattle-2-Spokane ride over Hwy 2, and those riders get done in one day in July ... so, yes, it is eminently ride-able.
I think if you search around here you will find some suggestions for taking the Old Highway 2 route over Stevens Pass - leaving the main road at Scenic, just west of the west portal of the long RR tunnel - cars can't make it, but there is supposed to be a pedestrian/bike bridge there. That section would be interesting, but might not agree with 23mm wide tires very well.
You'll see a really interesting variety of the geography, that's for sure.

How are you planning to split the days up / where in general were you thinking of staying?