I would like to know if it is appropriate to install chair rail in a foyer area in which there are no chairs.

Appropriate isn't really the right way to look at it.
If YOU like the idea and look, then go for it.
After all it's YOUR house and Everyman's home is his (her) castle..

If you are going for some authentic restoration then you leave the rail out. However, Like Curlyben points out, if it's the look you want then go ahead. There are no hard and fast rules about chair rails anymore, once functional now mostly for looks. Unless you are on some hostorucal register its your call.