Cleaning it will only be a problem if the product is soft. If it can support being hit with 90PSI air without bending at all it will be easy to clean. Depending on the type of copper used it should sustain 90PSI very easily.
The hardness of the structure can be many times lower than the hardness of the material when you're talking turning it into FOAM. Compare the hardness of steel wool and steel.
If this is anything like I'm envisioning, you could probably take a 3" block of the stuff and step on it and crush it down to about 1/4-1/8". And unlike traditional material foam, this stuff isn't going to spring back.
Even if it can survive the blast of air, it may just serve to drive the particles deeper into the block. A filter has to be thin or very porous to insure air pressure can drive most of the trapped materials out.
I'm betting the best way to deal with dust/dirt in this case is to simply filter the air very well. Very fine dust should be removable with air, but you don't want anything at or above large dust particle size getting into that foam or you'll never get it out.