Yep, I'd expect this.
I have another tank that was set up as a fry tank, with an inert gravel substrate and a few plants. It had bad BGA and other algae problems, I'm sure because of poor nutrient levels. After a few months I got sick of looking at it as it was. I treated the algae problems and dosed it to bring the NO3 and PO4 levels up to a reasonable level. Since then the 30 well-fed, adult guppies in that 10 gallon tank (I know, too many) seem to be producing what the plants need, because they are growing well without any additional dosing, and there is no algae problem.
Ahhh, now you are thinking!
I intend to set up a tank using the method that Tom outlined, as soon as I can find a local source that sells Equilibrium in less than 5 year quantities.
In fact, maybe two tanks: one with fish and one without.