Yes, they will touch up chips and scratches. "Paint correction" means doing everything possible to remove existing blemishes on the paint job you have. They can work miracles on completely removing blemishes and swirls which are in the clear coat layer. Anything that has penetrated into, or removed, the base coat color can't be fixed without adding paint. A good technician can do a great job w/ touch-up paint, but don't expect it to be completely perfect.

I suppose the ultimate "paint correction" would be a complete "re-spray."

Jeez, you are massively over-thinking this! You have a white car, stop worrying about it. You probably don't even need much more than a few dots of touch-up paint, and good wax job.