Hi,
You can join windows 2003 to a domain with functional level Windows 2016.
Windows 2003 doesn't support SMBv2, so you have to enable SMBv1.
For your information, Windows 2003 is out of support , I recommend you to install a server using a supported operating system and avoid enable a weak protocol like SMBv1 and RC4.
Please don't forget to mark helpful reply as answer