Most cherry varieties are indeterminate. What variety are you growing? You can prune as long as it is an indeterminate variety.
I agree it looks a bit wimpy from lack of light, but if it seems healthy, it will probably keep growing if cut back. And providing better light and other growing conditions will result in healthier growth.
I would actually NOT cut off all the suckers because generally, the secondary sucker growth can be more vigorous. Look for thicker, vigorous suckers lower down and pick maybe 3 or 4 maximum to keep, then top/cut off the rest -- especially the weak growths.
The plant might be more manageable after pruning and this might be the time to move it if you can. But if you are going to keep it here, I think you will have better results if you lined the two side walls with Mylar (I use emergency blanket) and then install two 4 ft shop lights vertically. 2-tube lights for total of 4 tubes would be better. Use 6500K daylight tubes.
You can train/support the 3-4 vines by wrapping around strings hanging from the ceiling. Give them plenty of space to spread out. Keep the suckers pruned.