I agree with the general opinion that you need to let the audience (those people who consider themselves part of the audience) applaud when they want. I have been to a few performances where the performers asked the audience to hold their applause and it seemed to work but there was a definite connection between the numbers that held it all together. Applause would definitely have interrupted that.

The year before last we produced Tommy at the Chocolate Church. We deliberately ran the first act so fast that the audience had no opportunity to applaud. When the act wrapped up with the big number in the pool hall and the music crashed to an end the audience, who had been held back for the whole time, literally exploded into applause and cheers. If you think you can manage something like that then you should go for it.