It’s possible, but extremely unlikely. Think about the way in which DNA becomes a trait:
1. DNA is a sequence of nucleotides (AAATTCCGATCG . . . )
2. These get turned into RNA (UUUAAGGCUAGC . . . )
3. In this RNA, each group of three nucleotides codes for a particular amino acid. But if you do a little math, you will notice that in the first position, you can have any of four nucleotides (A, U, C, or G). In the second position, you can have any of four nucleotides again. And in the third position, you can have any of the three nucleotides again! So that means you have:
4×4 x 4 = 64 possible combinations of nucleotides. But we only have 20 amino acids!!!! What this means is that different combinations of nucleotides can give you the same amino acid!!!!! (This is called “degeneracy.”) So, for instance, tyrosine can be built by RNA that goes “UAU” or “UAC.”
So we have gotten as far as going from DNA to RNA to amino acids.
4. The amino acids form proteins…
5. ...and the proteins twist and coil together in just the right way to give you….pretty much everything in your whole body.
SO! If you have the right degenerate amino acids, you could have a different DNA sequence coding for the same amino acids, which could give you the same proteins, which could give you the same trait. But consider that not all amino acids are degenerate, so you can’t just run around substituting left and right.
The likelihood of this working out in nature to strikes me as vanishingly small. But you could probably build it in a lab just for kicks, if you had about a thousand years of free time.
Did that make sense, and was that at all what you were thinking of, or did I just go off on a ridiculous tangent?