As far as i know the 'apt-get' installs from the repos and 'wget' installs from a provided url (internet/http) so it should not matter if you remove 'wget' or not wether 'apt-get' works or not. I'm no expert so this is just what i know and i might be incorrect

If you remove 'wget' you wont be able to install NITdroid with the autoinstaller, but then again you could allways install again and see if your problem were gone