Wow that is a great offer! My mom actually had the same offer many years ago and she bought a loaded SUV with a $500/month payment (that was a lot in 2001)...a few months later the company closed up shop and she was stuck with the payment. Not saying that will happen to you, just a cautionary tale to be sure that you are able to make the payments on your own just in case.
As far as your questions...you have not given us enough information to provide you with any solid advice. You currently have a car payment for your current car, correct? What is the remaining balance? What are the monthly payments?
What is your credit score? What is your annual salary? How much debt to you carry (student loans, credit card debt etc)? These might seem like personal questions but it will help in answering your questions. Many, many, many people have two or even three car loans. Those individuals usually have excellent credit and/or a high salary (and/or a low credit to debt ratio).
If you make a decent salary and are able to meet all of your credit obligations, and you have a good FICO score with no recent baddies, then you should have no trouble obtaining a second car loan while you still have an active loan with a balance. Think of it this way, people trade in cars with balances owed everyday and the banks issue a new loan for the new car without the old car being paid off as a condition of being approved for the new loan.
As far as paying off your current loan first and it helping your credit...I do not think paying off that loan first will really make a difference in your score for obtaining the new loan. In fact, it is good to have a mix of credit which involves installment loans.
The only issue I could see is if you have a lot of debt with a smaller salary; a bank or CU might see that as a reason to not issue you a second car loan. But you will have to provide us with more info.
