There is no way to prevent the program from detecting identical matches. In most instances that's the exact purpose of these programs!

As to whether that will affect your downstream results, it depends on what you mean exactly by I am going to be combining the query and significant targets together into a model. If you mean that you plan to build a hidden Markov model from your query + identified sequences, then it doesn't matter that some sequences in your alignment are going to be identical. Model building procedure automatically down-weighs identical (and even very similar) sequences, so the net effect will be as if you did not have duplicates.

If you want to convince yourself that this is a case, make an alignment of two identical sequences - or 10 identical sequences, for that matter. When you run hmmbuild on that alignment, it will print a summary saying how many sequences are in the alignment (nseq), followed by how many effective sequences (eff_nseq) are there. No matter how many identical sequences you put in your alignment, the eff_nseq will be 1 at most, but more likely smaller than 1. That means even though the alignment has X number of sequences, the HMM building program will act as if it has seen only one of them. Even for large alignments of non-identical sequences, say 2000 of them, eff_nseq will rarely go into double digits unless your sequences are truly diverse.