It depends entirely on what it is and what it does.
I would certainly not recommend using Outlook 2003 in 202x, but then, I would not recommend running Outlook, full stop.
But using Word, Excel and Powerpoint 2003 today, on local files? Yes, that is pretty safe on an updated and secured PC.
First, you must install Office 2003 SP3:
https://archive.org/details/OFFICE_2003_SP3_INST
Then you are fairly safe.
It is very noticeable that if you install the "Microsoft Office Compatibility Pack for Word, Excel, and PowerPoint 2007 File Formats" – still available on the Internet Archive:
https://archive.org/details/file-format-converters_202107
... then this installs a lot of extra stuff, and that means the PC suddenly needs lots of extra security updates.
So if you don't need it, don't install it.
Me, I use Word 2003 and nothing else. All my other needs are served perfectly well by LibreOffice Calc, Impress, etc.