Not necessarily. Advertising has diminishing returns -- we know this because companies don't buy unlimited advertising. If every ad dollar was as good as the first (i.e. it generated more than a dollar in profit) then everybody would buy an unlimited amount of advertising so they could make an unlimited profit. At some point you hit saturation and it costs more than it makes you.
Meanwhile the little guy needs it more because they're unknown, i.e. their baseline is further from the point of saturation so they have a higher cost/benefit ratio. If nobody advertises then people keep buying from the incumbent because they don't know of any alternatives.
The biggest problem with advertising isn't big vs. little, it's that it's a signaling war. If Coke spends a dollar and Pepsi doesn't, Pepsi loses $2 in sales. But if they both spend a dollar then they've each burned a dollar only to both stay where they started.
What would really help is to have some industry of trustworthy third parties whose job it is to tell you what to buy, but nobody has ever really cracked it, because the buyers don't want to pay for it and the sellers only want to pay if it will influence the results.
Those may be quite different things.