Yes it will. "Antibiotic" is just a name for a particular kind of antibacterial compound that's put in a pill and given to sick people so it can work inside their bloodstream. The general point about bacteria evolving resistance applies to any antibacterial chemical, not just the ones in pills.

[Edit: It's possible that by "soap that is merely antibacterial without using antibiotics" you mean just ordinary soap, with no chemicals added; but that's not what the article is talking about, it's specifically talking about triclosan, an antibacterial chemical.]