Single photon avalanche diode (SPAD) has recently been introduced as a powerful detector for long distance underwater visible light (UVLC) communication. In this paper, the performance of the SPAD detector in UVLC is analyzed considering the effect of the turbulence induced fading resulting from air bubbles in addition to the combined effect of attenuation and scattering. Automatic repeat request (ARQ) system is adopted to mitigate different underwater impairments and reduce the error probability at the receiver side. Approximate packet error rate (PER) expressions are derived using Laguerre Gauss polynomial for a finite number of transmission. Next, the average energy efficiency and throughput are analyzed to account for the increased energy consumption cost and the decreased effective transmission rate, which results from adopting the ARQ scheme. Finally, different numerical results are introduced to verify the derived PER expressions, demonstrate the ability of the proposed ARQ system in extending the transmission range, and show the trade-off between energy efficiency (EE) and throughput.