In the context of your question, whether there is a thrust-enhancing ground effect either during take-off or terminal landing, the answer is apparently "no".
Citing "Mars Exploration Entry, Descent and Landing Challenges" (2006) by Braun and Manning:
"Terminal descent thrusters can not spend
any more than a few hundreds of milliseconds within a meter or so of the surface without digging trenches, launching small rocks into the landing gear and producing destabilizing ground effect backpressure on the bottom of lander."
Also, from "Tradespace Model for Planetary Surface Exploration Hopping Vehicles" (2012) by Philip M. Cunio:
"After this, development proceed with the production of a quick-release launch stand, which
minimized stand dynamics and ground effect during launch. This enabled launch and hover
testing, as, shown in Figure E-9."
(These are verbatim quotes from the papers, grammatical and punctuation errors intact.)
I found two other papers which may contain relevant information ("Development of a terminal landing rocket system for Apollo-type vehicles" by Jack F. Lands Jr. 2012, and "Investigation of Effect of Ground Downstream of Overexpanded Dual-Bell Nozzle During Vertical Takeoff and Landing" by Yonezawa et al 2010), but haven't read either of those, and the previous two citations seem to give us the answer.
You obviously know about aircraft ground effect. Helicopters also experience an "in ground effect" increase in performance when hovering somewhere within one main rotor diameter of the ground. This is because the rotor wash compresses the air beneath the rotor, increasing the air density and allowing for an increase in lift characteristics for the "rotary wing" in a similar way that a fixed-wing aircraft experiences an increase in lift when close to the ground.
Rockets don't experience this effect in the same way because they do not work on the principle of aerodynamic lift. The turbulence generated by the thrust serves to destabilize the vehicle rather than enhance its performance.