Not in the slightest. Notice in The Walking Dead they really don't discuss 'the beginning' often, mainly because we live in the era of Twitter and it simply isn't realistic that a huge percent of the population would turn to zombies so quickly.
The second that strange things started happening, *everyone* would know it. If it began in a city, that city would be cordoned off. If it began as it was portrayed in TWD, many people in morgues and funeral homes would die, and everyone else would get out of dodge. We wouldn't need much convincing.
Cities are surrounded by countryside in most places (save southern California, etc), rapidly slowing down the speed the disease could travel and allowing containment.
There's just no realistic scenario where an infection like this could spread so far so fast *unless* there is a gestation time of, say, months. If over 90% of the population was infected before they realized, it could happen, but outside of diseases we've been dealing with for generations (like Shingles), nothing works along these lines.