Making such sweeping statements about biotechnology in general is impossible if you ask me.
Even when limiting oneself to agrobiotechnology it is impossible to make such statements because there are so many different crops that have been developed.
It is true that first-generation biotech crops are mainly developed to increase productivity, for example to resist insects (Bt maize) or to be able to be used with herbicides (Roundup ready soybeans). And yes, that may push down prices but as you point out that may also free-up labor for e.g. other more valuable crops. And of course an important question is whether or not farmers will actually adopt or be able to adopt the crops. The final outcome is a general equilibrium question, that cannot be easily answered.
There is quite a bit of research on the impact of individual crops in individual countries. See e.g. Qaim's: The economics of genetically modified crops in the Annual Review of Resource Economics or the meta-analysis by Klümper and Qaim in Plos.
Moreover there are second generation crops that address other issues such as drought and vitamin deficiencies where studies argue that benefits far outweigh potential costs, e.g. Wesseler and Zilberman's The economic power of the Golden Rice opposition in environmental and development economics.
Now this is not to say there are no negative effects of GM crops, they do for example cross-over with local weeds, resulting in herbicide resistant weeds. Similarly the built-in pesticide in insect resistance of GM crops, may result in resistance of those insects to that pesticide, but then again resistance problems occur anyway, independent of we use "normal" pesticides, "natural" pesticides or GM crops. Reducing resistance probability requires careful planning, buffer zones and integrated pest management.
Also the increased productivity may mean that land that was previously marginal can now be used for crop production at the expense of e.g. tropical rainforest. Then again the increased productivity also means that we need less land for the same production. Again the net effect is an empirical question.