A bit earlier than that, I think. Remember that the first satellites were launched for the IGY in 1957, and perhaps someone in this world will decide to play around with the things by then.
Only because there were all these big missiles around for throwing nuclear warheads. Without an IRBM/ICBM race, you won't get satellites for a long time--if ever.
And yes, Viking was a sounding rocket. Made by the Navy. For developing ballistic missile technology.
Make no mistake--the Space Race was a side effect of the ballistic missile competition. If there's one thing I've learned from being a space historian, it's that.