A "bird" with mammary glands would obviously be interpreted as a completely different lineage than other birds. This lineage may have developed mammary glands independently following a split in the common ancestor of early modern birds.
Then we would expect to see analogous structures instead of homologous ones. For example, no one would think that a butterfly wing is more homologous to an eagle's wing than a gull's wing. We can determine that a gull and eagle wing are homologous structures while an eagle and butterfly wing are analogous structures.
Common design, on the other hand, has zero explanation for the observed nested hierarchy. There is absolutely no reason why we should see a mixture of reptile and mammal features but no examples of a mixture of bird and mammal features in a common designer scenario.
Even more, you are have a massive case of projection. We do observe a nested hierarchy which is evidence for evolution. You try to explain away the evidence, trying to claim that it really doesn't exist when it really does. You then invent completely made up scenarios for reasons why you refuse to accept the evidence. You are doing the very thing that you claim scientists would do, even though they haven't.
In any case, it's really lame to lay out an alleged potential falsification like this only after bids have been well studied and no evidence of mammary glands has been found.
The prediction of matching phylogenies between sequence and morphology was predicted more than 50 years ago, before the data was in.
"It will be determined to what extent the phylogenetic tree, as derived from molecular data in complete independence from the results of organismal biology, coincides with the phylogenetic tree constructed on the basis of organismal biology. If the two phylogenetic trees are mostly in agreement with respect to the topology of branching, the best available single proof of the reality of macro-evolution would be furnished. Indeed, only the theory of evolution, combined with the realization that events at any supramolecular level are consistent with molecular events, could reasonably account for such a congruence between lines of evidence obtained independently, namely amino acid sequences of homologous polypeptide chains on the one hand, and the finds of organismal taxonomy and paleontology on the other hand. Besides offering an intellectual satisfaction to some, the advertising of such evidence would of course amount to beating a dead horse. Some beating of dead horses may be ethical, when here and there they display unexpected twitches that look like life."
Emile Zuckerkandl and Linus Pauling, (1965) "Evolutionary Divergence and Convergence in Proteins." in Evolving Genes and Proteins, p. 101.
Rest assured that if mammary glands had always been present in birds, early evolutionists would have developed a narrative around that pattern. This is not hypothetical but certain.
They are still finding new feathered dinosaur fossils. Why wouldn't they also find fossils with feathers and a mammalian middle ear?
