A private key is just a 256-bit random number. (Well, a number between 1 and hex value FFFF FFFF FFFF FFFF FFFF FFFF FFFF FFFE BAAE DCE6 AF48 A03B BFD2 5E8C D036 4141.)
Where did you get that God awful number? The actual value of p for secp256k1 is:
p = FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFFC2F
= 2
256 - 2
32 - 2
9 - 2
8 - 2
7 -2
6 - 2
4 - 1
Oh, I see, that is the order n of G. You just copied the wrong number.
So yes, you could flip a coin 256 times and copy down the results into a 256 bit number and as long as your number is less than the (prime) number p shown above it is a valid private key.