This question is really hard to answer, because it is very vague.
Before going further, take a look at the observational evidence for dark energy. There are five lines of evidence, which are (copy/pasting from a previous question of mine on the Physics SE):
Supernovae. A specific type of supernovae (type 1A) are supposed to be standard candles - that is, their luminosity is known. In turn this lets us measure distance to faraway galaxies, check how fast those galaxies are receding from us, and check if that recession speed is increasing over time.
CMB. Data from the Cosmic Microwave Background indicates the universe is approximately flat. Visible matter + dark matter can account for ~30% of the energy content required to make the universe flat, leaving ~70% for something else - dark energy.
BAO. Baryon acoustic oscillations act as a "standard ruler" that lets us measure how the Hubble constant varies with redshift (i.e. time), and see if the recession speed is increasing with time.
Late-time ISW. ISW stands for integrated Sachs-Wolfe effect. The idea is that, usually, a photon that enters a potential well gains energy as it falls in and loses energy as it emerges, and gain/loss exactly cancel. If a universe is expanding in accelerated fashion, then this is untrue; the potential wells / hills are smoothed out and there is a permanent shift in the photon's energy and therefore temperature. If we see a correlation between hot and cold spots on the CMB and the locations of superclusters and voids, then it's a sign of accelerated expansion.
Galaxy evolution. This uses (known) evolution of early-type galaxies as a standard clock. Once we know how long it takes for a galaxy to evolve from one state to another, as well as their redshifts, we can reconstruct how the Hubble constant varies over time, and see if the recession speed is increasing with time.
This list sounds impressive, and it is, but note that all of the evidence here hinges on General Relativity as a frame assumption. In other words, if GR is incorrect, none of these lines of evidence hold up. Dark energy could very well not exist. This shouldn't be surprising if you think about it, since GR is the theory underpinning cosmology.
Then consider your question:
Or put into other words: If a different theory (e.g. modified gravity) was able to explain the accelerated expansion and was consistent with all other fully understood aspects of cosmology, would dark energy still be a useful concept?
If a modified theory of gravity is assumed, then dark energy might not exist. Or it still might - this is because any modified theory of gravity needs to reduce to GR in some limit (in the same way GR must reduce to Newtonian gravity in some limit). All five lines of evidence for dark energy would need to be re-examined. Some of them might hold up in the new theory, some might not. If some line of evidence holds up, then dark energy remains useful since it can (potentially) explain that line of evidence. If all of them don't hold up, then dark energy might be useless.
But all this depends on what the new theory is. Without details of that theory, we can't begin to answer the question. So the question "would dark energy still be a useful concept?" is too vague to answer.