Although I would love to believe such trials, if somebody only has one colony, numerous factors could be affecting production.
For example; Many of the reports I've heard about dubias producing better after having citrus go something like this:
"So my dubias haven't been producing since I got them, so I gave them some oranges, and yesterday I found babies!"
Now, one could say the citrus made them give birth. Or one could also say any fruit could have encouraged a female to drop her babies, especially after months of carrying an ooth and not having any.
The best way to go about testing this would be to set up several bins, starting with a batch of subadult nymphs (maybe 100 or so) in another bin. Per day, as subadults mature, they would be removed and put into corresponding bins in equal amounts (3 females and 1 male per bin per day, for example) to ensure that all the roaches are at the same level of maturity. From there, each bin could be given unlimited access to food/water and supplemented with select fruits on a schedule (the fruits could be offered in excess to allow the roaches to eat their fill.)