First of all I was not talking about beta decay from fusion because that was not the scenario you brought up, however I did incorrectly say beta- decay instead of beta+ decay.
Addressing your OP you said:
Alpha radiation consists of a He nucleus, so the neutrons and protons are 'fused' together. Let's assume we can somehow remove the neutrons from the nucleus. Your question then is could the 2 protons undergo fusion. The 2 protons are already fused together, so I'm not sure what your asking.
In reality if the 2 neutrons were removed from the nucleus the resulting helium isotope would be extremely unstable and one of the protons would immediately beta+ decay to a neutron forming deuterium. No fusion would occur.