ROTFL. Do you know what a working dog costs? Good luck with that. But you could try to build an artificial nose based on the headspace.
If you need to screen thousands of people per day as they're say, all going to the grocery store, or the office, or whatever, it doesn't take too many days of several thousand "tests" per day times say $1 per test to come up with $10k or $20k.
If a well trained dog that can do the test is $100k then yes you're starting to talk about an equivalently priced test to those already in the marketplace.
Covid tests require a significant amount of human and machine time such that they cost tens of dollars right now. I suspect that dogs could bring that down by an order of magnitude or more.
Taking into account he costs (dogs, transport, dog handler etc.) it does not seem to be a cost effective solution. Yes, fogs were used to detect pregnancies but we don't do this anymore.
But when your talking about a test being performed on thousands, potentially tens of thousands people per day, you would recoup the cost in no time.