Here's a macro (attached) that's not exactly what you asked for - xlist_symbols. It borrows some code from the list_symbols (bound to alt+dot for me) function to work out which operator to use but in doing so, it's forced to call AutoCompleteUpdateInfo() which has the effect of showing a list of member symbols as if you typed alt+dot. Also, if neither . or -> are valid, it tries .* and ->* too.
The code does not insert a "." character unless it thinks it's inserting a member access operator so you can't bind the macro to the "." key but you can bind it to alt+dot - or whatever key you have bound to list_symbols.
If you really want to bind the macro to "." you would have to change it slightly so that if you type 123. - it actually inserts a decimal point - or if you're in a comment or string.
If you want to try it, open xlistsym.e in the editor and load it using the load-module command in the macro menu.