Real quick here- the answer to your question is no. Phorid flies, unlike flesh flies/face flies/blowfiles, are not attracted to blood. They are target specific and have no interest in anything other than the imported fire ants.
Pesticide sprays are a big money maker for the chemical industry but as you've just experienced first hand, aren't all that effective. If you continued to rely on sprays, you'd end up in a vicious cycle repeatedly buying more and your home would end up chemical laden.
Go back to the articles I posted links to and re-read them all then go back over #14 of the very first link I posted for you. Is there any way you can post a photo of the ants that are getting into your home?
Re-invasion is inevitable. It's only a matter of time regardless of what method you choose to control them but phorid flies appear to be capable of providing the greatest relief for extended periods of time because they don't knock down native colonies of ants. Unfortunately, they're not cheap so you may have to take a second look at baits and how to use them properly so as to maximize results.
Here is a link to your extension service-
http://www.aces.edu/
They have a search engine and you can plug in the words fire + ants to see what comes up to learn as much as you can learn so you will be in a good position to make the best decisions for you. If it were me, I'd call my local extension office and let them know that you understand why it's important not to kill off any native ants and just come right out and ask them what they believe will work best for you in your particular situation but please share with them how much money you are in a position to spend to manage these fire ants so they don't suggest products that won't be affordable for you.
And I will re-read. Thanks for all the links.
