I do not know, would have to work it out, actually need Randy for that

It is less soluble as CaCO3 from what I can gather in FW.
CuCO3 = 2.3 × 10-10 Ksp
CaCO3 = 3.36 x 10-9 Ksp
So it is not as soluble as CaCO3 in FW. Cu can also combine with OH and give Cu(OH)2. If you add copper to a kalk solution this happens.
2Cu++ + Ca(OH)2 ===> 2Cu++ + 2Ca++ + 2OH ==> Cu(OH)2 + 2 Ca++
Cu(OH)2 = 4.8 ×10-20 Ksp, very, very insoluble
Kalk = 5.02 x 10-6 Ksp, very soluble
However, one needs to be very careful with these Ksp's. A Ksp really does not tell you how soluble soemthing really is. It tells you how much you can hold in solution. The general rule is the higher the Ksp the more that you can dissolve and teh faster it dissolves. For some salts, for example, you can hold allot in solution once dissolved but some are very difficult to dissolve. Case in point: I brought to Randy's attention long ago. Water can hold about as much Magnesite ( MgCO3) as Aragonite / Calcite (CaCO3) but it is even harder to dissolve than Dolomite ( Mg,Ca(CO3)2 ) which is the least soluble of the carbonates and which can hold little in water. We were kinda shocked when we fond this out.
Ksp = Solubility Product Constant. There is something that they never really give numbers on like Ksp called Ksc = Solubility Rate Constant. This is how much a salt can dissolve at x pH in y time. More of a true solubility value that we would be interested in, as it tells us how fast something dissolves and at what pH. Chemist really do not care about this and just want to know how much salt can be held in solution, as that is all that really counts. Ksp just means what its saturation is. So, Ksp of x salt = 100 % Saturation of x salt. That Ksp can be worked out with a chem algebra which you can convert into ppm saturation for that salt. Note; The Ksp found in almost all books are for Pure Water and not Seawater and yes, they are different.
Found this for you but no real numbers
http://www.epa.gov/nrmrl/wswrd/cr/pubs/ace2006.pdf