Hi,
English CV and cover letter are absolutely fine—I did the same when applying to OW and received both interviews and an offer. Most international consulting firms in Germany accept applications in English without any issues.
Just be aware that interviews, especially cases, will likely be conducted in German, so make sure you’re prepared for that part.
Happy to help you get ready for interviews in German. Feel free to book a free Intro call to discuss how I can help you!
Cheers,
Kevin