This is certainly possible with ITC - I suggest you place nanoparticle suspension in the ITC cell (which is stirred throughout the iTC experiment) and protein in the ITC injection syringe. If you have a colloidal nanoparticle suspension (that does not have nanoparticles settle over time) you can use that in the syringe. If you have an idea of the average diameter/surface area of the nanoparticle, and how many beads there are per ml of suspension, you can make a good estimation of number of nanoparticles in the iTC experiemnt check out this citation: http://www.pnas.org/content/104/7/2050.long
If you do not know this you can still do ITC
I also gave a webinar on the use of ITC to characterize nanoparticles you can get it here: http://www.malvern.com/en/support/events-and-training/webinars/W150205-microcalorimetry-nanoparticles.aspx
Before you try using nanoparticles in your ITC, please figure out how you will clean out the ITC cell
Depends on how much information you want to get out of the ITC experiment, if you just want to know if your protein binds to the np or not, or general nature of the interaction (exothermic/endothermic) then it is not necessary to know the MW of nanoparticles. However, without the information on MW or molar concentration of your nanoparticles, you probably wont be able to calculate the thermodynamic parameters like stoichiometry, binding affinity or changes in entropy etc.