I spent some time today finding out in which levels you can blow up the starting heli without failing the mission:

Of 30 mission total (Single|Campaign):

3(1|2) have you start in a boat instead but you can blow all of those up.

15(7|8) Don't feature a heli at the start, but one does have a heli for an allied unit that can be blown up.

3(2|1) can be blown up.

9(1|8) fail the mission, the single mission has another heli with friendlies and neither can be blown up.