Debt consolidation loans are one of those “half dozen on one hand, six on the other” type of thing. A loan is still a loan and requires being paid off in full.
Consolidation of loans to decrease your interest rate is one thing, consolidation so you are paying less each month is another.
Look at it from the point of view of the lender – why would they take on $23,000 of risk by themselves if there was nothing to gain? They are not nice guys doing it for the sake of being good to you.
They know if you are making a smaller total payment on your debt, you will be paying on it for more years. More years equals more interest in their pocket.
In regards to your question, no debt consolidation will not hurt your credit rating because you have the same amount of debt as before with a different lender. Qualifying would depend on your income level, credit rating, and a few other criteria individual lenders use to screen out likely deadbeats.
I have never heard of any perks for school teachers consolidating their loans, but that doesn’t mean they don’t exist.