The effects of Fe-bearing phases on the structure, mechanical properties, and fracture mechanism of a non-heat-treatable model sheet alloy (wt.%: Al–2%Cu–1.5%Mn(-Mg,Zn)), designed for Al20Cu2Mn3 dispersoids, was investigated. This involved a combination of thermodynamic modeling in the Thermo-Calc program and experimental studies of structure and mechanical properties. It has been shown that the addition of 0.5 and 0.4% iron and silicon leads to the formation of eutectic inclusions in the Al15(Mn,Fe)3Si2 phase. In addition to the Fe- bearing inclusions, the formation of the eutectic Al2Cu and Al2CuMg phases can be expected in the as-cast structure of the experimental alloys. Despite their relatively high fraction of eutectic particles, non-homogenized alloy ingots demonstrated sufficiently high deformation processability during the hot (400 °C) and cold rolling, which made it possible to obtain high-quality sheet alloys (with reduction degrees of 80 and 75%, respectively). The results of the tensile tests revealed that, after cold rolling, the addition of 1% Mg significantly increased the tensile and yield strengths, whereas the effect of 1% Zn was negligible. At the same time, the uniform distribution of Fe-bearing phases in the structure of the cold-rolled sheets contributes to the preservation of the dimple mechanism of the fracture toughness. This helps to maintain the same level of ductility for the cold-rolled sheet Fe-containing alloys as for Fe-free alloys. It has been shown, based on the data obtained, that adding Fe, Si, Mg, and Zn to the base Al–2%Cu–1.5%Mn alloy in a total amount of more than 3% makes it possible to retain the ductile fracture patterns of the base alloy and obtain a fairly higher level of mechanical properties. This suggests the fundamental possibility of using a variety of secondary raw materials (containing the main elements present in aluminum alloys of different alloying systems) to prepare a base alloy that does not require homogenization or thermal hardening.