You can do that since, it is a UNIX account, and u can telnet into it.
BUT........
I remember last year when I 1st got eggie 1.6.2, I had a nice webspace that allowed me 500MB's, and so I decided to do what you want to do. I uploaded eggie, compiled him and everything, about a month later, I got SHUTDOWN by my web host. They locked me out, and I had to go thru a whole lot of junk to get my site back online and operational.
The thing is, if u have webSPACE, you have to sign up for SHELL SPACE, (which seems stupid to me, since you already have acess to the damn shell). So to prevent you from getting shut down, I would NOT just do what I did, rather contact your provider FIRST and see if it can be done that way.