Oxygen bleaches, both perborate and percarbonate work perfectly well with enzymes. Indeed many of the first laundry pre-soaks such as Biz, and Axion were nothing more than perborate bleaches with enzymes.
Today all manner and sort of oxygen bleaches, from CloroxII, to Vanish, to FleckenSaltz, to Napisan all contain enzymes.
The only reason one could possibly see for an oxi-bleach dispenser is for when using very long wash cycles and one is washing colours, to keep contact time short to prevent fading.
However many if not most TOL laundry detergents are loaded with enzymes, and have oxygen bleaching systems. So not sure what benefit delaying adding even more oxygen bleach is going to have.
When it comes to bleaching with oxygen bleaches, unless one is using boil wash temps, longer contact time greatly benefits the bleaching action. Enzymes work best with a temperature range of 100F to 120F though many detergents now boast enzyme performance from 85F to 140F, so again not sure what purpose delaying adding enzymes would have as again, longer contact time give better results, especially if one is going to be allowing the washing machine to heat water to hot or boiling wash temperatures.