It would be helpful to see at least the whole of that sentence. However unless there is a surprise like "... if he hadn't lost his voice" or something, I can see no obvious reason for the use of "would".
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Mr. TomWhy does the speaker use would here?There are at least two possible reasons.
Mr. TomMr. Frank would come on stage now and highlight our new policies unless there are no bored faces or droopy eyelids.That is not spoken by a native speaker of British or North American English.
Mr. Tomunless there are no bored faces or droopy eyelids.I really don't know what message the speaker is trying to convey here.
I really don't know what message the speaker is trying to convey here.Neither do I.
Mr. TomMr. Frank will come on stage now and highlight our new policies unless there are no bored faces or droopy eyelids.As well as the problem with "would", the speaker has got the use of "unless" mixed up. These would make logical sense (still may not be ideal for expressing exactly what was intended):