Is there an advantage? Yeah, probably. But, is it worth it? Well, maybe.

It's all the things combined that make it faster, though, and some (most, all) of those things don't require a tri bike. Lighter frame, more aerodynamic, aero bars, race wheels (on some bikes) or just light/nice wheels.

I would plan on using your current bike the rest of the season, but it can't hurt - much - to ride one and see if you like it.