But it doesn't work quite that way. You would need to be able to search against those fake profiles for very specific allele combinations, and GEDmatch can't do that. I'm on less firm footing here about admixture/ethnicity than on protein-producing genes, so I'll stick to that; the principle, though, will be similar.
Your genome has a little over 3 billion base pairs, and the typical genetic genealogy test looks only at about 700,000 of those, or about 0.023%. There are a lot of areas along the chromosomes that have no known direct effect on us; those areas seem to have no active function and are often referred to as "junk DNA." A lot of those 700,000 base pairs the genealogy tests look at are in junk sectors for a very good reason: alleles there are more freely able to mutate without causing possible harm to the organism, and those are places we can look at to help differentiate the otherwise 99.9% DNA that all human beings share.
The protein-producing genes that affect bodily structure and function typically vary in length from just a few thousand base pairs to, rarely, about 2 million. A very few are larger than that. GEDmatch can't report on information down to the gene level. And within that protein-producing gene, a mutation that changes its coding is the result of only a few alleles or even a single one, a single base pair.
There's a massive amount of assumptive math that goes on in genetic genealogy that's unique to the field. Medical and forensic genealogy isn't concerned with trying to estimate crossover frequencies and guess at possible relationships in generations. Heck, even the start and stop points for a physical segment you see reported by GEDmatch (and others) does not reflect actual base pairs and alleles. They're estimates only, because the data are working with defined SNPs that represent, again, only about 0.023% of the entire genome. The start and end points of a segment are estimated by the closest matching SNP...and that could be thousands of base pairs from the actual loci.
We search and evaluate based on centiMorgans. This isn't a physical measurement at all. It uses linear extrapolation to estimate the recombination frequencies based on the location on a particular version of a human genome map, male or female...and the two differ significantly. The centiMorgan is way to estimate and present relative genetic distance in terms of relatedness, and the computed values differ greatly depending upon which chromosome is considered, and the (again, estimated) start and stop points on that chromosome. One cM may be equivalent to tens of thousands of physical base pairs in one place (rare), or a few million base pairs in other places. An unusably tiny, to genealogists, 3cM segment might well contain 10 million base pairs.
And the "integrity" of the reported segment is also an estimate. You know when you go to look at one-to-many or one-to-one matches in GEDmatch, it has one field to set the minimum number of SNPs and another to set the maximum "mismatch bunching" limit? The integrity of a physical segment is assumed if a minimum number of SNPs match sequentially (and no-calls, base pair values that came out of the test with a null value--there typically are around 0.5% to 1.5% of these--are ignored in the evaluation) with some wiggle-room from that mismatch bunching limit. A segment computed to be 7cM may have, say, only 1,000 SNPs tested along a stretch of chromosome 10 million base pairs long. So we're guessing that all those millions of intervening base pairs are identical because the relatively few that we samples, the SNPs, are, mostly at least, identical in a contiguous string.
That's the granularity and, frankly, "iffiness" with which genetic genealogy works. GEDmatch can't find individual genes, much less the individual allele mutations that might affect a medical condition. If a few alleles impact a gene and those base pairs are not a tested SNP, they could change all day long and estimates used to arrive at our genealogically-relevant segments would never know it.
Specific example. Diabetes is not thought to be a genetic disease. However, studies have shown that the risk of developing Type 1 may be increased by particular variants of the HLA-DQA1, HLA-DQB1, and HLA-DRB1 genes that live in the HLA (human leukocyte antigen) region mostly in chromosome 6. In genetic genealogy, this is a well-known "pile-up" region, meaning that most humans "match" there in the current technology of our testing. The HLA genes provide instructions for making proteins that play a critical role in the immune system. Kind of a big deal, and wholesale mutations in that area mean not-so-good things for the survival of the organism. Ergo, most of us match along that area of chromosome 6. You could construct a fake genome that included appropriate values for HLA-DQA1, HLA-DQB1, and HLA-DRB1, and upload it to GEDmatch...with zero information resulting.
I had to go look this up, without much to show for it. I found that the Illumina Human1M-Duo BeadChip--now discontinued and not a population (genealogy) purpose chip, but a medical one--looked at a grand total of four base pairs (technically, reference clusters) in the HLA-DQB gene; none in DQA or DRB. I can't find any indication the Illumina OmniExpress or GSA chips--the ones used in autosomal DNA testing today--test for any base pairs in the HLA-DQ or DR genes at all.
I know that diabetes was only a random, top-of-the head example. I'm not singling it out. I just wanted to go from the macro to the micro to illustrate that the reporting we can get from GEDmatch has pretty much zero possibility of linking results to disease, and that those reported results--unless using the for-purpose admixture tools--are also probably of no value for identifying ethnicity. Mind you, there are companies like Promethease who can take your uploaded raw data and provide some information about non-genealogical stuff, but that's what they do; they don't do genealogy. And you can't extract the medical stuff from GEDmatch.
