Will mitosis occur in the absence of interphase?

The answer is no.

Without the interphase period, a full-fledged process of mitosis is impossible. This stage is very important, since during its period important processes of cell preparation for division take place. For example, during this period, the cell accumulates the necessary resources for the next division, the hereditary information is replicated, the cell centers are doubled. If we assume that for some reason the interphase disappeared, then at the same time the property of living organisms to self-reproduction collapsed.