I'm not a real estate appraiser, and I don't know Detroit (except by reputation). However, here are a few observations:
Real estate investors do what you're describing all the time. They buy low, rehab, and then (in a buy and hold situation) take some cash out.
Yes, of course the appraisal should be higher after you fix up the property. The appraisal will be based on what comparable properties are selling for. So, to use your scenario, suppose you buy a property for $15,000 and put $30,000 into the rehab. And after the rehab, it would sell for $80,000, based on sales of other nearby comparable properties.
Lenders have gotten a lot stricter with cash out refinance, which is what you're talking about. Another avenue might be a HELOC. Or you could even create a second mortgage and sell the note (though I wouldn't recommend that).
You should check with a mortgage broker to find out what lenders are willing to do these days. How much will they refinance for? (80%? In that case, you'd be able to refinance for $64,000, thus pulling $19,000 out). And seasoning is a big question. A mortgage broker should be able to help you with those questions.