Yes. Access 2007 can run an Access 2003 database without needing any
modification.
There are some differences, of course. For example, Access 2007 uses a
ribbon, so any custom menu/toolbar you design turns up as an option on the
ribbon. And there's the usual issues with library references, e.g. if your
code references a specific version of the Office library. Details on library
references:
http://allenbrowne.com/ser-38.html
There are some security holes you may wish to plug if you anticipate your
database being opened in A2007. See:
Prevent Access 2007 users modifying existing databases
at:
http://allenbrowne.com/ser-69.html