Most compliance legislation says you need to be running a supported operating system and applications. Running Server 2003 after the end of extended support is an obvious compliance violation.
If you are being audited for compliance after the EOS date, auditors will be on the lookout for computers running Server 2003 just as they will be on the lookout for computers running Windows XP. If your organization does have a custom support agreement from Microsoft, you’ll be in the clear. But if you are running Windows Server 2003 as an unsupported operating system, be prepared to have your compliance assessment be less than positive.
Many IT Pros tend to think of non-technical issues like compliance as ephemera that they don’t need to worry about as part of doing their job. Depending on the compliance legislation that an organization is subject to, being found to be in a non-compliant state can actually cost the organization a substantial amount of money. If you are having trouble motivating higher-ups to provide you with budget around migration, you might want to point out that the penalties won’t be just technical if you get audited, they may be financial as well.