Zombies as in Romero Zombies, never going to happen, physically and biologically absolutely impossible, Infected zombie-like types as in 28 Days Later or WWZ, oh yes, very very possible. With an outbreak of Infected like those, if the outbreak isn't contained immediately then it really would only be a matter of time before everyone is infected. As we have seen time and time again with commutable infections the incubation period can vary widely from individual to individual, locking down Airports and Ports may not necessarily happen fast enough to contain the infected, if it were an outbreak here in Britain it only has to get to Europe and in no time at all it could be a Worldwide pandemic.
I guess there is a very small chance of surviving the outbreak and out-living the infected if absolutely all the right moves were made, but to emerge from your hiding place into what, surviving would almost certainly be worse than falling victim to the infection.