Actually, with the exception of Tuscany, it was expected that the local rulers in central Italy would fall, as they nearly did 1848-49, and Napoleon III had agreed in advance that Sardinia could claim those territories.
On the use of privateers...the US is going to find them much less effective than in 1812 for several reasons:
1) Privateers need ports or friendly coasts and the US in 1862 has far less than it did in 1812.
2) They need ships and manpower and both will be less available because the US navy in 1862 is much larger than in 1812. At least for the moment.
3) They need friendly ports abroad to resupply, repair, do business and so forth and there won't be many ports willing to offend the Royal Navy on such matters. This also touches on the issue of privateers being out for profit and a lack of such profit will have an impact.
4) Additionally the Royal Navy will not be nearly as distracted as in 1812 and will likely further reduce the ports of the US by blockade or worse soon.
There is also one other issue which may trump all of the above. The Union in 1862 has tens of thousands of men assigned to the blockade, and even more if the landings at New Orleans took place. The blockade is doomed but the men and much of the equipment can be saved if removed in time. Lincoln's sensible move would be to evacuate all those men and as much equipment as possible as soon as possible. That will require all the shipping which can be mustered.