If that had happened, it would have been very interesting, the reasoning being that when Vegeta first heard about Frieza getting the Dragon Balls on Namek, he had no choice but to reveal his card that he was taking Frieza and his entire empire on in a declarnation of war. In this scenario, if Vegeta heads to Earth, then he could still be stealth about his crossing Frieza. He would arrive on Earth, Bulma, Krillin and Gohan would have already been gone, there is a good chance possibly Goku also. The events of Namek would still play out with Krillin and Gohan saving Dende and getting a Dragon Ball from Guru, they would have likely hidden out until Goku arrived, since they could suppress power levels and only really Vegeta had the ability to sense power levels without the scouters.
Frieza may not have called for the Ginyu Force, reason being is that Zarbon and Didoria would still be alive and clearly superior to the challenge ahead, it was basically getting the two pesky Earthlings. Frieza brought the Ginyus in when he understood that Vegeta was getting stronger and had taken out his two right hand soliders and his possible alliance with the Earthlings could be a problem in him getting immortality. It is likely that Vegeta would be racing to Namek after learning that everyone is gone and figuring out they have gone to Namek to get the balls, it is also very possible that Frieza himself may ask Vegeta to come to Namek and join him by his side, since at that point Vegeta had not crossed him.
Vegeta then could have put a scheme together to take the Dragon Balls through deception.