A UV/IR cut filter can be helpful when doing EAA, but only under certain circumstances:
1. If you are using an achromatic refractor or camera lens, then you will see a large benefit in the sharpness of your image using a UV/IR cut filter. The reason for this is that achromatic telescopes and lenses are designed to give a well focused image of visible light only. Cameras used for EAA are also able to effectively "see" UV and IR light, so on achromats and lenses you get a fuzzy out of focus image.
2. When viewing emission type nebulae (H-II regions, planetary nebulae, supernova remnants), adding a UV/IR cut filter will improve contrast by removing light pollution in the IR band. This is true for any light pollution level. Adding a UV/IR cut filter when viewing emission nebulae also helps to highlight the nebulosity by reducing the visibility of stars. It is beneficial to stack a UV/IR cut filter with an LP filter for this application.
3. When viewing galaxies under dark sky conditions only (Vm +6 or better), adding a UV/IR cut filter can help improve the image contrast by a small amount. If there is any light pollution it is better to not use any UV/IR cut to view galaxies.
4. When viewing solar system objects (Sun, Moon, planets), adding a UV/IR cut filter can help to reduce the appearance of atmospheric turbulence (seeing), making it easier to achieve a good focus and providing a steadier image.
If you can afford it, I recommend getting a good performing UV/IR cut filter. The best I have tested is the Baader Planetarium version. It has measurably superior performance to all the others I have encountered. Cheaper brands are available, but those brands don't give the same high in-band transmission, and don't come with anti-reflective coatings to eliminate halos and other contrast affecting issues.