Is it possible? I have Outlook 2013 but Word 2013 is so packed with things I don't need, such as collaboration tools, layout, document design, that it's a nightmare to use. Honestly, for me, Microsoft Word reached it's zenith with 2003, Word XP, and has gone wonky since then.
I'm confused. Are you saying you're running Word 2003 with Outook 2013?
I don't have Word 2003 but I installed Office XP with Word 2002 and it seems to work fine other than I couldn't seem to get Outlook 2002 to connect to the Outlook.com server. Everything else I tried worked, Excel, Word, Access, PowerPoint all opened and could open and close files. I didn't test them thoroughly but didn't encounter any errors on anything I tried.
About a year ago I wanted to get an IMAP account to sync with my cell phone. Outlook 2003 wouldn't do IMAP. I got Outlook 2013. I had Word 2003 to write my emails and embed photos and then send by Outlook. I could also use Word 2003 for personal documents. I had a problem that required me to remove Word 2003 and decided to wait till Windows 10 to put it back on. And, I was having trouble. I tried again this morning and got it loaded. I'm testing now but it worked with Outlook before, too. Oh, I never did get the friggin' IMAP account to work on my computer with Outlook 2013.
I would consider moving to 2010 or newer for Office, since Microsoft has been killing off support for older releases. I believe to get it running you need .NET 2,3,3.5 which can be installed as follows
Press the Win Key
Uninstall a Program
Turn Windows features on or off
Check the box for .NET Framework 3.5 which also includes 2.0 and 3.0