You bet. One of the beauties of the No.1 is its flexiblity as to caliber.
I might suggest thinking about the twist rate of the new barrel, for years the 10 twist was it for 17's in general. Lately some of the newer longer tipped 25gr bullets for the 17 really like a 9 twist. Of course if going to the heavier(30gr++) 17 bullets, more twist is required. If had a choice of twist for my shooting requirements in the 17, I would choose the 9 twist and not look back.
My 17 bumble bee in a No.1 has a 10 twist Shilen, it does ok with the older Hornady and Remington bullets that I have around; today I would up the twist to 9 for the newer, longer tipped bullets like the Vmax.