This is the silent killer. Even if you manage to install Chrome 49, the browser cannot negotiate modern TLS 1.3 connections. Most of the web today (Google, GitHub, AWS, Azure) requires TLS 1.2 at a minimum, with many servers disabling older ciphers. Chrome 49 will throw ERR_SSL_VERSION_OR_CIPHER_MISMATCH errors on 90% of HTTPS websites. You effectively have a browser that can only visit plain HTTP intranet sites.
However, for years, a workaround existed. Because Windows Server 2003 64-bit shared the same kernel core as Windows XP Professional x64 Edition, Chrome installers designed for Windows XP often worked on Server 2003. Between 2009 and 2014, many admins successfully ran Chrome 22 through Chrome 48 on their 2003 servers. google chrome for windows server 2003 64 bit
While Windows Server 2003 64-bit was powerful for its time (supporting more than 4GB of RAM), it had a notoriously poor ecosystem of 64-bit drivers and libraries. Chrome’s 64-bit sandboxing mechanism relies on security features (like SEHOP and ASLR improvements) that were still immature in Windows 2003 x64. Early experiments with Chrome x64 on 2003 often resulted in frequent sandbox crashes or blue screens. This is the silent killer