Monte-Carlo modeling of effective area and count rate of the TAIGA-IACT Cherenkov gamma-ray telescope unit with an upgraded camera based on SiPM OnSemi MicroFJ-60035 detectors and optical filters SL 290-590 and SL 290-590 has been carried out. It has been shown that with the SL 290-590 filter the threshold detection energy of the telescope would be improved compared with its current PMT-based configuration and would reach about 0.4 TeV. With the narrow band UV filter SL 290-590 the estimated threshold would reach about 0.7 TeV, which is a reasonable value for a 10 m2 class IACT, especially because with a SiPM-based telescope it will be possible to carry out observations during moonlit nights and at twilight without a substantial increase of the threshold. One may conclude that an upgraded TAIGA-IACT unit will be an efficient instrument for studies of TeV-band gamma-ray emission of various cosmic objects.