Well, no, they couldn't. The very fact you are saying that shows you know nothing about genetics. I'm not in a position to give you a primer here (google is your friend) but suffice to say it has NOTHING to do with existing defects and everything to do with a viable gene pool. Which cannot be maintained with a baseline taken from two people.
This is spot on, it's simple biological fact that you can verify by taking even the most bare bones foundation course. Nor does it rely on faith or my opinion. You don't avoid genetic defects by creating a larger genepool through inbreeding, it just doesn't work. All you are doing is creating more muddy waters. No matter how many children they had they would still be working from the genetic material of two individuals and empirical science has shown us that doesn't work. Period.
We don't avoid incest purely because of religion (although historically the church has acted as avaluable mouthpiece to strengthen the taboo), nor is it because there are too many "genetic defects" in the pool, but because doing it creates those defects. By your model the human race simply couldn't have thrived the way it has.
There's little point me repeating this ad nauseum, either you are willing to do a primer in genetics in which case the answer to your question will be clear, or you aren't and are prepared to accept the word of your minister who I am prepared to bet good money is not a biologist.
Your argument seems to rest on that "with God everything is possible" but you don't seem to grasp the idea that for many of us God is not a given. If you are going to make sweeping statements starting from a premise you have to establish a consensus that said premise is valid, otherwise you are on the road to nowhere.
As I have no evidence for the existence of God nor logical reason to even suspect His existence I see no reason to accept such a statement in denial of hundreds of years of painstakingly careful scientific study. You may believe God makes anything possible, but that is your belief. The fact you believe it does not mean others do, or should.
In this case for instance, if someone does not believe in God (or remains unconvinced), why then would they be impressed by such a statement when all the empirical evidence really does stack up to the contrary. Evolution by natural selection happens. We can recreate it under lab conditions. It happens and by definition requires a large enough genepool to allow for significant genetic variety. Two people is not enough, nor does the literal creation story explain how we happen to share so much of our genetic make up with every other species on the planet. No matter who is offended by that idea and froths at the mouth trying to terrorize you into believing otherwise it is simply true beyond any reasonable facsimile of doubt.
That doesn't preclude God from the story and Darwin was a religious man himself. He saw no conflict between the two and despite my personal misgivings about the Christian church (or any other organised religion) neither in principle do I. If God did create us he had to do so somehow and the evidence suggests that natural selection was it. If so fair play, any intelligent creator would far more likely start life by building the basic principles into His universe than by just dropping two specimens arbitrarily into a world which clearly wasn't compatible with them. (Forbidden fruit? The Serpent? Original sin?)
Bear in mind I have had a fundamentalist upbringing myself, as I said. I'm actually grateful for it, much as I am grateful for the polio and tetanus inoculations I got as a child. It left me as an adult far less likely to be swayed by "arguments" which prey on people's insecurities and fears rather than reason.