To answer your question directly NO if you just called an paid of the Loan it will not show positive payment history, it would be a foolish move.
If you paid the loan off in full, the default status will remain on your record/ credit report which will disqualify you from government mortgage loan program such as FHA. Your best option is to get the loan out of default before paying it off. You can accomplish this by consolidating the loan or completing the rehab program. I personally would complete the rehab program, because you get two benefits the default status will be removed plus your credit score will increase once the default TL is removed from your report.
I was in the same boat as you a few months ago, my loan was in default the balance was only $3000, I completed the success 9 months of payments but was waiting for the Department Of Education to fine a buyer for the loan. I applied for a conventional loan and was approved, my plan was to pay off the loan if it came up during the underwriting process. In the time it tock me to fine a home they found a buyer for the loans, it only tock 30 days for all the negative information from the Department of Education to fall of my credit report my score with up 40 points. If I was you I would hold off till you completed the rehab program. I am so happy I completed the rehab program.
