It turns out that that's a completely different meaning of "homology".
"Homology" really just means something like "correspondence". So it has, among its meanings,
1. the one in the article here: a way of associating topological spaces with algebraic structures, so that you can study one by studying the other.
2. the biological one: instances where two (parts or aspects of) living things are similar on account of common descent.
It's not 100% impossible that the two notions might come into contact with one another. DNA can become knotted, and there are enzymes called topoisomerases that enable DNA strands to pass through one another to unknot them. (Maybe something similar happens with proteins?) Knots are topological objects and homology is one of the tools mathematicians use to study them. Perhaps one day it will turn out that particular DNA or protein sequences tend to lead to particular sorts of knotting that are biologically significant (e.g., maybe they control the transcription rate of DNA or the shape of proteins), and perhaps it will turn out that they are selected for, and then perhaps from time to time biologists will find regions in two organisms' DNA or proteins that exhibit mathematically similar kinds of knotting because they're descended from an ancestor that found that kind of knotting useful. In that case they would have homology in their homology.
"Homology" really just means something like "correspondence". So it has, among its meanings,
1. the one in the article here: a way of associating topological spaces with algebraic structures, so that you can study one by studying the other.
2. the biological one: instances where two (parts or aspects of) living things are similar on account of common descent.
It's not 100% impossible that the two notions might come into contact with one another. DNA can become knotted, and there are enzymes called topoisomerases that enable DNA strands to pass through one another to unknot them. (Maybe something similar happens with proteins?) Knots are topological objects and homology is one of the tools mathematicians use to study them. Perhaps one day it will turn out that particular DNA or protein sequences tend to lead to particular sorts of knotting that are biologically significant (e.g., maybe they control the transcription rate of DNA or the shape of proteins), and perhaps it will turn out that they are selected for, and then perhaps from time to time biologists will find regions in two organisms' DNA or proteins that exhibit mathematically similar kinds of knotting because they're descended from an ancestor that found that kind of knotting useful. In that case they would have homology in their homology.
(Probably (k)not, though.)