We study the young star cluster populations in 23 dwarf and irregular galaxies observed by the Hubble Space Telescope (HST) Legacy ExtraGalactic Ultraviolet Survey (LEGUS), and examine relationships between the ensemble properties of the cluster populations and those of their host galaxies: star formation rate (SFR) density (ΣSFR). A strength of this analysis is the availability of SFRs measured from temporally resolved star formation histories that provide the means to match cluster and host galaxy properties on several time-scales (1–10, 1–100, and 10–100 Myr). Nevertheless, studies of this kind are challenging for dwarf galaxies due to the small numbers of clusters in each system. We mitigate these issues by combining the clusters across different galaxies with similar ΣSFR properties. We find good agreement with a well-established relationship (MVbrightest–SFR), but find no significant correlations between ΣSFR and the slopes of the cluster luminosity function, mass function, nor the age distribution. We also find no significant trend between the fraction of stars in bound clusters at different age ranges (Γ1–10, Γ10–100, and Γ1–100) and ΣSFR of the host galaxy. Our data show a decrease in Γ over time (from 1–10 to 10–100 Myr) suggesting early cluster dissolution, though the presence of unbound clusters in the youngest time bin makes it difficult to quantify the degree of dissolution. While our data do not exhibit strong correlations between ΣSFR and ensemble cluster properties, we cannot rule out that a weak trend might exist given the relatively large uncertainties due to low number statistics and the limited ΣSFR range probed.