mxyzplk's answermxyzplk's answer is spot on. Just adding more specifics:
Would this be an advisable tactic?
Definitely yes. There is significant potential benefit and really no harm or risk.
Or would there be any consequences? I feel like this could be like a very mild case of extortion.
That would be highly unlikely. As a hiring manager I would very much prefer be kept up to date. I can choose to act on it or not, but I certainly would appreciate the info and a chance to react. It's better than just getting an offer rejected or the candidate disappearing.
Also, what could be a good example email that Alice could send to Company A and B?
Hi"Hi Bob. Thank you so much for interviewing me and I'm very excited about the position and the opportunity. I understand that this process takes time, but I currently have a competing offer on the table and I need to make a decision by XYZ date. I'm very interested in a role at and it would be really helpful for me to understand what your expected timeline is. Would it be possible to discuss this on a quick phone call ?"