A drive-by-download can refer to several things.
- A download that happens with the user's consent, but they didn't really understand that the consequences.
- A download that happens without the user's consent or knowledge
The first method is not very "drive-by" in my opinion, but it is still useful to recognize that this is still possible.
Tricking someone into downloading a file can be as simple as them thinking they are clicking a regular link and then downloading an EXE, PDF, etc. You don't need JS or a plugin to do this, but it helps. A very simple example would be a "popup" (just a piece of html styled with CSS to look like a popup) that says "you have a problem with your computer, click ok to download a fix." Clicking this would initiate the download of an EXE, that the user may or may not run.
The second method is a little more rare, and little more dangerous because it can affect even the computer-savvy user. This often involves some sort of exploit in the browser/OS itself or a plugin (flash, adobe reader, etc). NoScript would prevent any exploit that relied on javascript/plugin that was hosted on a domain that was not whitelisted. So if you whitelisted security.stackexchange, and someone hacked into the server and added malicious JS, then you would not be safe from this. NoScript will also not protect you from any other OS/browser vulnerabilities that do not get blocked by NoScript obviously. Take for example, the Windows Metafile vulnerability. It required no JS/plugin and allowed for arbitrary code execution on the victim's machine.
The basic answer to your question is that, yes, drive-by-download is still possible with noscript installed. Even technically possible with javascript and other plugins disabled. However, keep in mind that it still helps to mitigate the threat.