Just the reverse; it should HELP your rating.
The exception to this is; if you owe a debt, (credit card or loan) and you keep it current, and keep the balance below 20% of the limit, you will have a continual good report to the Credit Agencies.
The exception to this is; if this balance increases you Debt/Income ratio too high.
The credit rating improving will depend. If it was an installment loan you paid off early, it really won't affect your score either way as now you have a loan that was paid off and will now report as closed.
If it was a revolving account like a credit card then yes your score will improve dramatically as it will show you have your entire credit line available, if you have paid off a revolving account be sure the account is not closed. As a closed account will decrease your score(s).