Short answer: No.
Long answer:* The Counterparty address was obviously hand-picked; the odds that the Counterparty burn address was generated randomly are 58^27, which means that it is effectively impossible the burn address was generated randomly which also means that the private key for the address is unknown.
Essentially how such addresses are generated:
- Start with some sort of obviously nonrandom string (1CounterpartyXXXXXXXXXXXXXXX)
- Append dummy checksum to string (e.g. 111111)
- Base58 decode the above to get network version + RIPEMD160 hash + “checksum”
- Find the checksum that corresponds to a valid address
- Output the valid address, which has neither an associated pubkey or privkey
Note that as long as this address doesn’t spend coins (it can’t), even quantum computing will fail to make an appreciable difference.
Essentially, if coins are spent from such addresses, then Bitcoins from any address can be spent.
For more information, see this Stack Exchange answer: http://bitcoin.stackexchange.com/questions/9408/how-does-vanitygen-calculate-difficulty.