The normal recommendation for someone in your friends general position is to attempt the ESTA application, and if it is denied (which it almost certainly will be), then apply for a visa. There would be no downside to applying for the ESTA in a situation like that.
However in this case, she has already applied for the visa, so things are a little different.
The actual situation is likely a little different to what you've described. Generally the consulate would not "investigate some details of something", and it's unlikely there would be a second interview.
Far more likely, what's actually occurred is that your friend was found ineligible to obtain a US visa, and her application was denied. That doesn't so much mean that the US consulate staff decided not to give her a visa, it means that she met one of the criteria that under US law actually mean she is not eligible to obtain a visa. In this case, the staff have no choice in the matter - she is ineligible, and thus her application has to be denied.
Once her application is denied, there is a process that can be followed to request a "Waiver of Ineligibility", which is basically a request to have the issue that makes the person ineligible for a visa ignored - thus leaving them eligible to obtain a visa (but not, directly, granting them one). The fact that the consulate staff allow this option means they consider that there is at least a chance the waiver will be approved - but it's far from a certainty. It also means that the consulate staff have determined that, other than the issue that made the person ineligible, the person would otherwise likely be eligible for a visa.
Waivers of Ineligibility generally take many months to be processed (6+ months). If (and it's very much an if!) it's approved, the consulate staff will be notified, and in most cases would simply approve the visa based on the previous interview - although they may choose to re-interview the person instead.
Now, to your specific question of whether it's worth applying for an ESTA. In this case, no. It's not. In addition to having to answer 'yes' to the question regarding arrests/drugs, your friend would also have to answer 'yes' to the question regarding having had a US visa previously denied. Plus of course the US immigration systems will be aware of the previous visa denial. The odds of the ESTA being approved is, literally, zero. Doing so probably will not impact her pending waiver of ineligibility, but given there is no chance of approval, it simply makes no sense to even try.
