My gosh, of course! You can make a great Berliner in under a month, easy. Kettle sour 2 days, ferment 7-10 days, carb 14 days. What's that, 3.5 weeks? It won't be as complex as a Brett Berliner, of course, but it can be great all the same. And if you're going to add a shot of syrup, the Brett surely makes much less difference.
There's a LOT to learn about kettle souring a Berliner Weisse, so you have some reading to do.