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Yes—indirectly. An updraft by itself is vertical air motion, so it does not directly change groundspeed; groundspeed is determined by your horizontal velocity over the Earth, while airspeed is your velocity through the surrounding air. Wind affects groundspeed, whereas airspeed itself is not affected by wind. rotorcraft.arc.nasa

If altitude is maintained

Entering an updraft tends to make the helicopter accelerate upward unless you correct. To hold altitude, you normally reduce collective/power (and sometimes make small attitude adjustments). That change primarily manages vertical force, not horizontal speed.

If you keep the same heading, pitch attitude, and indicated airspeed, your groundspeed should remain essentially unchanged unless the updraft also has a horizontal wind component—as turbulence commonly does.

Why groundspeed can change anyway

In actual convective or terrain-induced lift, vertical currents are rarely purely vertical. You can see a groundspeed change when:

For example: at 90 KIAS with no horizontal wind, a 500-fpm updraft does not magically make you faster over the ground. If you lower collective enough to remain level and hold 90 KIAS, you should still be near 90 kt groundspeed. But if that same rising air has a 15-kt tailwind component, groundspeed becomes roughly 105 kt.

Rotor-system consideration

A vertical gust changes the airflow through the rotor and can alter rotor-blade angle of attack and thrust. In strong turbulence, the practical technique is generally to use an appropriate reduced turbulence airspeed, hold a stable pitch attitude, and make small collective/power changes to stay within a safe altitude block rather than aggressively chase every vertical-speed fluctuation. Updrafts can be significant because they increase rotor-blade angle of attack, with the retreating blade particularly vulnerable if conditions are severe. aopa

So the short operational answer is: maintaining altitude in a pure updraft does not inherently change groundspeed; accompanying horizontal wind and the control inputs needed to stabilize the helicopter are what may change it.