Yes you will have a problem! I had a car in my corporation name and it even caused a problem at the border. I have driven down to the Yuc 5 times and was loaded with stuff.
About 20 mi from the border you will encounter a check stop.. that's usually where some guy will tell you you have something that you did'nt pay duty on and that you have a problem. 20.00 us solved mine. Get used to it in MX. But it does not work at the border. ie. McAllen-Brownsville. The last time I went thru there is one in-between that was better. At least it is fairly aggravating (Fluent Spanish helps a lot--I had none). Take the eastern most route and dont' forget the insurance. Sanborn has a helpful guide.