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In recent years, action-detected ultrafast spectroscopies have gained popularity. These approaches offer some advantages over their coherently-detected counterparts, enabling spatially-resolved and operando measurements with high sensitivity. However, there are also fundamental limitations connected to the different process of signal generation in action-detected experiments. Specifically, state mixing by nonlinear interactions during signal emission leads to a large static background which can obscure the excited-state dynamics. This could severely limit the applicability of action-detected spectroscopy to study energy transfer in larger systems. Here we perform fluorescence-detected two-dimensional electronic spectroscopy (F-2DES) of the light-harvesting II (LH2) complex from purple bacteria. We demonstrate that the B800-B850 energy transfer process in LH2 is barely discernable in F-2DES, representing a ~6.2% rise of the lower cross-peak intensity. This is in stark contrast to measurements using coherently-detected 2DES where the lower cross-peak reveals energy transfer with 100% contrast. We explain the weak presence of excited-state dynamics using a disordered excitonic model with realistic experimental conditions. We further derive a general formula for the presence of excited-state signals in multi-chromophoric aggregates, dependent on the aggregate geometry and size, and the interplay of excitonic coupling and disorder. We find that, dependent on the excitonic state structure, the excited state dynamics in F-2DES can be visible even in large aggregates. Our work shows that the signatures of energy transfer in F-2DES can be used to directly infer the excitonic structure in multichromophoric systems.