What can you tell me about this pedigree?

I just found the pedigree for the untrustworthy red dun QH we got at auction in November. Her great-grandfather was Peppy San, and her great-great-grandfather is Doc Bar (twice over). Those are the only names I recognized (I have minimal experience with this). Are they too many generations away to matter much?

Rockin T Lee Red Quarter Horse

To make a long story short, my friend bought this horse and has been boarding her "rescue" at the farm where I used to ride, on the condition that the farm owner got "first dibs" on the mare when she was ready to find a new home. We're hoping the farm owner doesn't want the mare and we'll be able to move her to a new barn with a trainer that specializes in horses like her. If her pedigree shows that she's got great bloodlines, the farm owner may not be willing to let her go. How far removed would great bloodlines need to be to not really mean much?

On a related note, the mare is in foal. If the sire of this foal is homozygous black (we're told he's pure Friesian, for the sake of simplicity I'm assuming he's not a fox), what are the possibilities? I don't know enough about genetics to be able to read her pedigree that way.

Thanks! I appreciate the help, I find this all fascinating!

I know nothing about QH bloodlines in Australia, let alone the US lol.

In terms of colour, assuming the sire is homo for black, you would have a 100% chance of a black based foal. So that's a start. Then you can have a 50% chance of dun from the dam, assuming that she is hetero and not homo. Add into the mix agouti, which without testing you can't see on the dam (sire doesn't have it if he is black). Possibilities are: black, grullo, bay, bay dun.