Here's the thing, there really isn't any substitution for pull-ups. Even lat-pull downs on a machine don't work all the same muscles as pull-ups.
So, to answer your question about using the elliptical machine as a substitution, sure you can if you're just starting out and as long as your goal is to eventually incorporate pull-ups. Can you do any pull-ups right now or is the problem finding a place to do them? Any local parks with pull-up bars or monkey bars or some place to do pull-ups? Local school playgrounds are a good place to look as well.
Bottom line is better something than nothing but you won't see as good results as doing pull-ups.
I have found 6 places to do pull-ups:
1. Home (door gym) - thinking about putting up permanent bar outside somewhere
2. Local park (can do pull-ups on monkey bars)
3. Another local park (has actual pull-up bars in three heights)
4. Work has a pull-up station by the soccer field
5. Work has a gym with two separate pull-up stations
6. School near work has "Fitness Area" with pull-up stations.