Would that indicate that there's still something else wrong with the notebook, or can an external faulty hard drive cause a BSOD?
Yes, there might still be a problem with the laptop. Yes, an external faulty hard drive can cause a BSOD. The two are not mutually exclusive. All the BSOD proves is that there is still a problem. The details of the BSOD can more specifically indicate what the problem is, but the mere presence of the BSOD itself doesn't tell you what the problem is.
If the laptop operates without error, without the hard drive in question, and ONLY shows the BSOD when the drive is connected, then that would indicate the issue is most probably with the drive. If you connect the drive to another computer and you get a BSOD on that machine, this would most certainly prove it out. However, if you connect other USB storage devices to the laptop and still encounter the BSOD, then you would have to point to the laptop as having the issue, as opposed to the hard drive. Of course, if connecting other USB storage devices causes a BSOD on the laptop, and the external drive also causes BSODs on other computers, then you see that both could be causing issues.
In short, there isn't enough information to say exactly what the problem is. Connect the drive to another computer. Connect other storage devices to the laptop. See what happens.