The short answer is yes. The long answer is, it is an ongoing PITA.
1. you need to install the software in version order. So, the oldest must be installed first.
2. you must take care of where they are installed so they are kept separate.
3. As Doc mentioned Windows has one file association table so you might be ok if 2003 always opens .mdb's and 2007 always opens .accdb's. Otherwise, you must either use a shortcut that opens the version of Access you want to open and pass in the db name as an argument. Or, just manually open the version of Access you want to work with and then pick the db to open.
4. I'm not sure when this was fixed but for a few years, Access used to also fight with itself over control of the registry. So, whenever you opened Access and it wasn't in control of the registry, you would get all these scary "installing" messages.
The preferred option is to use VM's and that allows the two to be completely separate. Or if you have spare PC's, and you only use the older version rarely, then separate PC's also works.