Yes. It's a known issue with titanium exhausts depending on several factors. Expensive titanium is expensive and generally less likely to crack, but cheaper titanium with crack inevitably but is more accessible.

You need high quality titanium like Grade 9 used by Akrapovič et al., argon-purged welds, thicker tubing, and such. Grade 2 tends to crack the most but it's easier to weld and affordable to buy so it's what a lot of cheaper titanium exhausts are made from. Titanium will absorb oxygen if it gets hot enough developing a brittle outer layer called an alpha case. Thermal cycling exacerbates this issue as it gets more rigid and more likely to develop microcracks under vibration. Cracks will develop near welds, thin-walled areas, or anywhere that's contaminated.

I would personally never spend my money on a titanium exhaust. It takes one bad weld or section and it's donezo, and titanium isn't as easy to repair as stainless steel. Imagine you get a car with an OEM titanium exhaust that cracks 20 years down the line and the part isn't made anymore, or you bought a one-off exhaust and the company doesn't exist? Good luck.