It's likely not going to make a significant difference either way. The biggest factors to your mortgage are going to be a reliable income, your debt/income ratio (smaller is better), and the loan-to-value ratio (smaller is better). So long as you're not stretching your income too much, the student loan isn't going to be a huge factor.
In addition, paying of a loan account is different that closing a revolving credit account (credit card). Closing a revolving account increases your utilization (how much you've borrowed versus the total of all credit limits), which is what hurts your credit score. Closing a loan account does not impact your utilization, but does reduce your total amount borrowed, which should improve your score.
If there are some negative factors from closing out the debt (which I doubt there are), they will likely be offset by the reduced debt-to-income ratio. You'll be better off saving as much as you possibly can for a 20% down payment, which will determine how much house you can afford to buy. Having 20% down will also save you a lot in your monthly payment, since you won't have to pay mortgage insurance (PMI)
All that aside, debt is not a game. Don't play around trying to improve a score that you have no control over. Remember that these scores are partially supported by banks and credit card companies that make money when you pay interest, so they obviously want to encourage yo to borrow more. Don't borrow money that you can't pay back very quickly for anything other than a house, and make sure you pay your bills on time. Then your credit score won't matter. Your income won't be sucked away by debt payments, and you can invest, build wealth, and not worry about your credit score,.