In other words, does half life have a correlation with decay energy of a beta particle?
The short answer to this question is yes.
The reason is wrapped up in "weak universality": the idea that all weak interaction at low energy share a common underlying process that controls the one of the two factors that go into determining rates for spontaneous processes. That leaves the phase space available to the products as the thing that almost solely determined the lifetime.
In short the phase space available to the interaction depends to a large degree on the total energy and to a much smaller degree on the mass of the recoiling remnant nucleus.
I gave a rather more complete treatment in another answer about the free neutron lifetime.