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If you get an offer from another firm and you only have a short period before you have to respond to it, you should definitely let the other firms know. It is quite a common circumstance and many of them will be willing to speed up the process. In some cases, I have anecdotal evidence of firms actually looking more favorably on candidates in this situation - I have been told that certain Magic Circle firms have a policy to immediately progress to the final stage candidates with a an expiring TC offer from a reputable firm.

However, if you think the time you will have to consider an offer will be very short (say, less than a week) you might want to email the other firms once you got the final stage interview invitation. This is a less common situation, but I still expect at least some to try to be flexible. Regardless, I do not see any circumstance in which you telling them about the situation will be held against you, so I do not think there is any reason not to try it.