Hi Jordan,
There arent any tests I can think of, not that it can't be done, but because there is no money in it. I would assume that the testing for horses was developed because of the sport of racing horses. There is alot of money in knowing the genetic makeup of the prize race horse. I don't think that there is a big enough market for the development of this test for ornamental plants.
As far as "Ghost" being all white there are a few possibilities that I can think of. First it could be that exactly what you stated, 'Saffron' has white, so this lack of pigment was translated into the flower of its offspring, making it white. Another idea I have is post transcriptional gene silencing is taking place. It may sound like a mouthful, but it explains why you see those two toned (white and purple) petunias at the nursery. Post transcriptional gene silencing (we'll abbreviate it as PTGS) occurs when a specific RNA sequence (the precurser for protein formation, including pigment) is degraded by enzymes before it can be translated into the protein that it was encoded to make. In the case of these petunias, breeders wanted to make deep purple flowers, so they crossed plants that over expressed anthocyanin (the protein that makes flowers purple) hoping to have a more purple flower. What they found was the offspring was white or had some degree of whitening in it. In theory it makes sense, cross purple with purple and make more purple. What they didnt take into account was the RNA transcript to make anthocyanin is double stranded and was produced in great abundance. The plant reconized these transcripts as being foreign (viral RNA). Plants have a very good method for destroying this ds RNA. First this enzyme called dicer cleaves the long anthocyanin ds RNA in to short strands. Next these short strands are incorporated in the RNA induced silencing complex (RISC) After this incorporation, another enzyme destroys the RNA. This in effect prevents any pigment protein from being produced even though the gene for the protein is functioning normally.
PTGA could explain why 'Ghost' is white when both of its parents are not. The plant's genes for pigment may be silenced. I would be interesting to see what offspring would be produced by this flower and if any are white. This is one instance where I think backcrossing could be used to figure out why the flowers are white. If it is a recessive gene, then you should see many more offspring share that trait when it is backcrossed to the parents. If it is PTGA, the offspring may not be white at all. It is possible that backcrossing it may cause white offspring because of PTGA, but it is unlikely.
It would be really interesting to cross 'Ghost' with 'Byron Metts' and observe those offspring. If the same recessive gene is responsible for their white color then the offspring should be all be white. If they are pigmented it could be possible that PTGA is to cause of the pigment deficiency. It is also possible if you get pigmented offspring, that the recessive white genes were in different loci in each variety, so one may have a dominant gene in the place that the other is recessive. By crossing them you produce a heterozygote that has pigment, but is a carrier of the white gene. Another idea is they have different types of mutations in the pigment producing pathway and when they are crossed you effectively fix that pathway, allowing pigment to be produced.
There are soo many different possibilities as to why 'Ghost' is white. It is going to take quite a few crosses to see if what gene or mechanism is the cause. Until then we can just enjoy the flowers
I think I might have ranted too much here, and this is more than anyone wanted to know, but this is what 3 years of genetic research and a different medium will do to you

-Chris