Q In a qPCR assay using probe, would non-specific amplification be possible occur in a situation of very high concentration of non-target DNA? 

During specificity test of a diagnostic, when it challenged against plasmid DNA from a non-target species at a very high concentrations of DNA non-target (10E8 copies/ul) there was amplification. However, at lower concentrations this did not occur. Non-specific amplification may have occurred due to stochastic events, ie, since all the components necessary for amplification to occur occur (except for the target DNA), the physical interaction between the molecules could have favored non-specific amplification, considering this extreme situation of High concentration of non-target DNA? 

A In short, yes, it can happen. 

In real-time PCR assays that are designed to be very sensitive you can sometimes have amplification of a nonspecific target. There are several possibilities. Real-time PCR assays, although often more specific than conventional PCR assays because of additional specificity provided by the probe. However, some assays will tolerate one or more mismatches in the probe and/or primer sequence. One possibity, then is amplification of a phylogenetically related organism that has a similar sequence. 

In a qPCR assay using probe, would non-specific amplification be possible occur in a situation of very high concentration of non-target DNA?