ECDSA recover on arbitrary values
Yes. 

Non-ethereum elliptic curve signatures result in the numbers r and s, both of which need to lie in the range [1,n-1], where n is the size of the order of the elliptic curve base point. See Wikipedia - Elliptic Curve Digital Signature Algorithm. 

Ethereum transaction signatures, use the secp256k1 curve (which has a fixed n value) and requires the numbers v,r and s. r has the same range as above, however unlike standard elliptic curve signatures, s is restricted to the range [1, n/2+1] (see the Ethereum Yellow Paper - Appendix F). Any values of r and s outside these ranges will generate an invalid signature. 

Assuming we stick to r and s values within this range, we must also supply a v value for an Ethereum transaction signature. EIP-155 specifies v = CHAIN_ID *2 + 35 or v = CHAIN_ID*2 + 36. 

The r value represents the x-value of a point on the scep256k1 curve. Fundamentally, v, represents the parity (even or odd) of the y-value of the point given by r (i.e the corresponding x-value). This parity determines whether to use 35 or 36 in the specification of v above. The value v is used as the recoveryid or recid in this library for ECDSA recovery on line 89 which is used by go-ethereum. Incorrect v values may make this recovery incorrect and give invalid resulting public keys. Thus, if one were to keep v fixed, and randomize r and s (or equivalently, randomize all numbers) within their range of validities and we were to assume an equal chance of getting an odd or even number, we would expect on average, 50% of signatures to be invalid (because we have an incorrect parity).