The success of ground-based, high contrast imaging for the detection of exoplanets in part depends on the ability to differentiate between quasi-static speckles caused by aberrations not corrected by adaptive optics (AO) systems, known as non-common path aberrations (NCPAs), and the planet intensity signal. Frazin (ApJ, 2013) introduced a post-processing algorithm demonstrating that simultaneous millisecond exposures in the science camera and wavefront sensor (WFS) can be used with a statistical inference procedure to determine both the series expanded NCPA coefficients and the planetary signal. We demonstrate, via simulation, that using this algorithm in a closed-loop AO system, real-time estimation and correction of the quasi-static NCPA is possible without separate deformable mirror (DM) probes. Thus the use of this technique allows for the removal of the quasi-static speckles that can be mistaken for planetary signals without the need for new optical hardware, improving the efficiency of ground-based exoplanet detection. In our simulations, we explore the behavior of the Frazin Algorithm (FA) and the dependence of its convergence to an accurate estimate on factors such as Strehl ratio, NCPA strength, and number of algorithm search basis functions. We then apply this knowledge to simulate running the algorithm in real-time in a nearly ideal setting. We then discuss adaptations that can be made to the algorithm to improve its real-time performance, and show their efficacy in simulation. A final simulation tests the technique's resilience against imperfect knowledge of the AO residual phase, motivating an analysis of the feasibility of using this technique in a real closed-loop Extreme AO system such as SCExAO or MagAO-X, in terms of computational complexity and the accuracy of the estimated quasi-static NCPA correction.