This paper will answer your question.
http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0086175
Yes, the paper shows one can detect what is present but not how much biomass/abundance. I doubt one can use this approach for biomass/abundance in the open sea because the rates at which eDNA will enter the water and will degrade will surely vary with taxa, location and a host of other factors.
There was another neat paper where they looked at the DNA attached to sand grains but again this was a biodiversity approach rather than quantitation.
Naviaux, R. K. et al. Sand DNA—a genetic library of life at the water’s edge. Marine Ecology Progress Series 301, 9-22 (2005).
Although eDNA is very effective at detecting what species are present, estimating abundance / biomass is a much greater challenge. There are various papers that demonstrate this for single-species assays, but at a community level it's not usually possible to estimate abundance because factors such as primer competition during PCR may bias answers. Factors such as stock structure (a few large fish have a lower surface area: volume ratio and therefore shed less DNA per unit biomass than many small fish), habitat preferences, time of year and taxon-specific DNA shedding rate are all likely to introduce biases of their own that will affect an eDNA estimate of fish biomass. That said, eDNA estimates are unlikely to be much worse in these respects than conventional methods such as gill netting, as all conventional fish sampling techniques also contain various inherent biases.
What kind of environment are you sampling in?
When you reduce the environmental variability between sites (lakes), you can estimate relative abundace.
Do you know if it may be possible to do something similar on tropical streams?
Not exactly biomass but certainly abundance, in a real life lake environment.
https://www.researchgate.net/profile/Jianlong_Li4/publication/301550636_Environmental_DNA_metabarcoding_of_lake_fish_communities_reflects_long-term_data_from_established_survey_methods/links/571de48108aee3ddc56c6eb9.pdf
eDNA has been used in many environments including tropical systems, but obviously it depends on the exact question. See
http://www.sciencedirect.com/science/article/pii/S016953471400086X
Article Environmental DNA metabarcoding of lake fish communities ref...
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