It seems to me that every stem that is pruned on my pyracantha sends out at least 2 shoots from the point of pruning, so once they get started, they do bush out quickly, if you cut back a little as each shoot grows. This can be done throughout the year, but as laurieuk says, once it has berries, then really you want to prune to make a show of them.
Mind you, I don't know much about the different varieties, I have 'Orange Glow' which is quite vigorous, others might not be.