Is any press good press for a startup?

If a startup were to get some questionable press in the media, would it still be considered a good marketing strategy? Granted that negative press might tarnish a large company's brand. But wouldn't it still bring some customers to a startup to make it worthwhile?

It depends, if the bad press is because of a buggy MVP then no worries, code and design can be fixed, if it is because of serious stuff such as ilegal business practices, sexual scandals or other huge red flags you may not just risk your startup but yourself and your other founders' names.

You should consider what would customers think about you but most importantly investors (if you ever want to get funded) since it could affect their decision to invest in your startup. All investors are going to google your startup as well as its founders to find out if you are trustworthy and their investment is worth it, going for the lowest risk possible.

In terms of SEO and promotion: yes, it's (almost) always welcome to get backlinks from reputable sources since Google still cannot distinguish sentiments accurately in its ranking algorithm.