While cell-to-cell variability is a phenotypic consequence of gene expression noise, sources of this noise may be complex - apart from intrinsic sources such as the random birth/death of mRNA and stochastic switching between promoter states, there are also extrinsic sources of noise such as cell division where division times are either constant or random. However, how this time-based division affects gene expression as well as how it contributes to cell-to-cell variability remains unexplored. Using a computational model combined with experimental data, we show that the cell-cycle length defined as the difference between two sequential division times can significantly impact the expression dynamics. Specifically, we find that both divisions (constant or random) always increase the mean level of mRNA and lengthen the mean first passage time. In contrast to constant division, random division always amplifies expression noise but tends to stabilize its temporal level, and unimodalizes the mRNA distribution, but makes its tail longer. These qualitative results reveal that cell division based on time is an effective mechanism for both increasing expression levels and enhancing cell-to-cell variability.