Following our recent work devoted to the effect of accretion on the pre-main-sequence evolution of low-mass stars, we perform a detailed analysis of episodic excursions of low-mass protostars in the Hertzsprung-Russell (H-R) diagram triggered by strong mass accretion bursts typical of FU Orionis-type objects (FUors). These excursions reveal themselves as sharp increases in the stellar total luminosity and/or effective temperature of the protostar and can last from hundreds to a few thousands of years, depending on the burst strength and characteristics of the protostar. During the excursions, low-mass protostars occupy the same part of the H-R diagram as young intermediate-mass protostars in the quiescent phase of accretion. Moreover, the time spent by low-mass protostars in these regions is on average a factor of several longer than that spent by the intermediate-mass stars in quiescence. During the excursions, low-mass protostars pass close to the position of most known FUors in the H-R diagram, but owing to intrinsic ambiguity the model stellar evolutionary tracks are unreliable in determining the FUor properties. We find that the photospheric luminosity in the outburst state may dominate the accretion luminosity already after a few years after the onset of the outburst, meaning that the mass accretion rates of known FUors inferred from the bolometric luminosity may be systematically overestimated, especially in the fading phase....