Does advertising increase consumer prices?
Indirectly, yes. We buy something, a portion of that something's cost is advertising. Advertising costs go up, so do the prices of $THINGs.
The cost of advertising your product on the Internet goes up - do you pass that onto the consumer? I don't think so - unlike manufacturing and distribution costs, which have to be absorbed somewhere, advertising is something that you choose to spend based on a balancing act of depressing sales because your product is more expensive and increasing sales because more people think buying it makes them look smarter or sexier or whatever.
I suspect as advertising costs go up, you look for cost savings in the advertising - for example doing less of it, perhaps more efficient targetting.