It might, but it might not. Generally, your company may be protected if the other company is attempting to or is invading your market. If the company operates out of another country, their website is in another language, and they are not operating in your market, you may have a difficult time proving damage.
To help avoid potential issues, you should diligently research your brand before filing your trademark. While performing your research, you may find companies that already exist in other countries with similar branding. If you are planning to market in other countries, you'll want to hire a legal team that can help you navigate foreign Intellectual Property laws.