No. In most parts of the world pyracantha grows outside. I did close a casement window on a firethorn hedge growing near the house once, trapping a bough indoors, but that is as close as I ever got to growing pyracantha indoors.
They grow outdoors in full sun, where they get 10-100 times the light intensity you'd find in a sunny window or a shady one.
http://aggie-horticulture.tamu.edu/...es/pyracan.html
I don't think anyone can tell you what kind of tree you have without seeing it. If you can and want to post a picture, go right ahead.