The electrical properties and deep trap spectra were compared for near-UV GaN/InGaN quantum well (QW) structures grown on free-standing GaN substrates. The structures differed by the presence or absence of a thin (110 nm) InGaN layer inserted between the high temperature GaN buffer and the QW region. Capacitance-voltage profiling with monochromatic illumination showed that in the InGaN underlayer (UL), the density of deep traps with optical threshold near 1.5 eV was much higher than in the QW and higher than for structures without InGaN. Irradiation with 5 MeV electrons strongly increased the concentration of these 1.5 eV traps in the QWs, with the increase more pronounced for samples without InGaN ULs. The observations are interpreted using the earlier proposed model explaining the impact of In-containing underlayers by segregation of native defects formed during growth of GaN near the surface and trapping of these surface defects by In atoms of the InGaN UL, thus preventing them from infiltrating the InGaN QW region. Deep level transient spectroscopy (DLTS) also revealed major differences in deep trap spectra in the QWs and underlying layers of the samples with and without InGaN ULs. Specifically, the introduction of the InGaN UL stimulates changing the dominant type of deep traps. Irradiation increases the densities of these traps, with the increase being more pronounced for samples without the InGaN UL. It is argued that light emitting diodes (LEDs) with InGaN UL should demonstrate a higher radiation tolerance than LEDs without InGaN UL.