No. Any web hosting provider even dedicated server can not provide you unlimited web space, unlimited emails, unlimited databases, unlimited add-on domains, unlimited alias domains, or unlimited bandwidth.
The cheap web hosting providers tell you they can provide you unlimited web space or unlimited bandwidth because you are novice. If you check the terms and you will find they can always say:
If you are using too much resources that it is causing ongoing performance problems for other sites, the cheap web hosting company will suspend your websites or throttle your traffic or require you to upgrade.