It's going to take us a few months to travel to mars in our spaceships. Will the relatively small size of the ship combined with a few months of "isolation" result in Mars being disease free until either we build bigger ships or faster propulsion?
Not completely, for a number of reasons, but in theory there should be less disease than on Earth.
Some diseases last for a very long time, like AIDS. Things like the flu will have a really hard time making it to Mars. Some diseases have few symptoms, which makes them easier to hide. Lastly, things in space just tend to end up really germy.
As a whole, with a bit of work, Mars could remain mostly disease free, however, proper precautions still must be taken.
For some comparison, the voyage time from Europe to North America was about 3 months early on. Disease still managed to cross that gap. No doubt the same thing would happen going to Mars, although I still suspect there would be less colds/ flu/ etc on Mars than on Earth.