Hi sdmark,
As dn has mentioned … the short answer is no. There are different ways to measure ILD (usually used for latex) or IFD (usually used for polyfoam) but ILD/IFD only measures firmness to a specific percentage of compression and the thickness of the layer (or mattress) that is being tested makes a significant difference. You could use a bowling ball or other very dense object to measure how far it sinks in to various mattresses as a relative softness comparison (although a bowling ball would probably be too light for a complete mattress) but this wouldn’t relate to ILD/IFD because the variable with this type of test would be the depth of compression on each mattress while with ILD or IFD the variable is the force used to compress it to the percentage that was being used by the test (usually 25% or 40% depending on the area of the world).
ILD alone is also only one of the specs that determines the softness of a material in “real life” because very few people sink into a mattress or a foam layer by exactly 25% and each material has a compression curve that gets firmer at different rates (compression modulus). The variance in compression modulus means that a mattress could be softer than another with a lighter testing weight but firmer than the same mattress with a heavier testing weight.
There is more about ILD/ILD in post #2 here and in post #6 here.
Springs don’t have an ILD and are measured by their spring rate. A cylindrical coil will have a linear response curve (vs foam which is more banana shaped and absorbs some energy as it compresses) but different shapes of springs or variable rate springs will also have a non linear compression. There’s more about innerspring rates and some comparison to foam compression curves in post #2 here.
The “bottom line” with all of this is that any home based method may be able to check a mattress for relative softness at certain compression levels (such as the bowling ball method) but this wouldn’t be comparable or “translatable” to ILD/IFD.
Phoenix