Instead of using an LED as a photodiode, consider using an LED as your light source and use a typical photodiode as your sensor element. This is a very common approach to solving exactly the problem that you are having, which is that you don't want to buy an expensive longpass filter for your photodiode.
This approach will work if you are making a transmissive measurement like absorbance or a reflectance measurement, since these require both a light source and a detector. It will not work if you are trying to measure an emissive source, like fluorescence or irradiance. If you are making an emissive measurement, you are going to need to use the longpass approach with a real photodetector. For low quantities, try Anchor Optics, Edmund Optics, Thorlabs, or Newport. Here's a 500nm longpass filter for $21.50.
To answer your question about the drawbacks of using an LED as a photodiode specifically... I think the major thing to consider for your application would be that if you want to use an LED as a photodetector, you can't assume that the spectral distribution its response is equivalent to the spectral distribution of its output. For instance, just because the output of an LED has a center wavelength of 600nm with a 25nm bandwidth may not mean that it is not sensitive to light at 450nm. I am not positive about this, but I would be absolutely shocked if that were the case.