Yes, but bitcoin's authentication is via ECDSA. Elliptic curve discrete log is solvable with Shor's algorithm, but the qubit calculation would be different.
Wikipedia seems to indicate that 2330 qubits and 126 billion Toffoli gates would be required for elliptic curves with 256-bit group size, although I wonder if the endomorphism of secp256k1 gives an additional speedup.
The question was about Shor's algorithm. The question relating to bitcoin seemed like an aside.
https://en.wikipedia.org/wiki/Shor%27s_algorithm
Given that the original article was about Quantum Computing, I was more interested in answering questions about Quantum Computing.