So... the easier definition of seq. Homology may be the degree of similarity between sequences, (In theory) indicating a shared ancestry. That is why you can build trees, becuase you suppose the sequences followed different evolutionary paths or duplication but originated from a common ancestor.

So, No, i dont't think you can use non-homologous sequences (I mean with NO degree of homology, otherwise they would be "weak" homologs) both for a logical and technical reason.

First, being non homologous they don't have similarity, though you cannot compare them and produce a tree. You can try to use a very large database of proteins and try to produce a tree with your database and a protein which you don't know to see if it clusters somewhere but would be easier to use blast.

Second, many programs like muscle, clustal and mafft implicitly “assume”

that the sequences you feed them are homologous. They just cluster together non-homologous sequences in a separate branch.

http://bioinformatics.bio.uu.nl/snel/BEG/PhylogenyOrthology_2013.pdf

Article An Introduction to Sequence Similarity (“Homology”) Searching

Thanks, dear Umberto Palatini for your valuable suggestions 

You can build different kind of trees, not phylogenetic. For instance composition based dendrograms. In this case you compare for instance the di/tri/tetra...nucleotide frequencies of the different sequences. But you will not get a phylogenetic tree. So, Umberto is right to say that you can't.

Thanks dear Matteo Brilli for your reply.