Q.Can I Root A Rose Of Sharon Indoors And Keep Watering Until Spring? It Has Roots Sprouting But I’m Not Sure If It’s Too Late
for outside planting in PA.

Certified GKH Gardening Expert
That will give it a better start! Doing so will extend its growing season, which will ensure a successful transplant in Spring. You may need a small horticultural light on it for about 12 to 16 hours per day. This will give it plenty of light to stay happy indoors. Misting, occasionally, will help.
Here is an article that will help once you plant it out:
https://www.gardeningknowhow.com/ornamental/shrubs/rose-of-sharon/rose-of-sharon-bush.htm