Not quite: According to the cosmological standard model, the visible universe will continue to grow (ie new galaxies will continue to come into view) - but only asymptotically, ie until a maximum size given by the comological event horizon is reached. However, the parts of the universe that aren't gravitationally bound to us will become fainter and fainter and increasingly resdhifted, and eventually, we'll be unable to detect other theoretically visible galaxies due to technological limitations.

There's a cosmological event horizon. Light emitted from within will reach us in finite time, light emitted from without won't. Similar to how a distant observer will never see on object falling into a (stationary) black hole cross the Schwarzschild horizon, we won't see galaxies crossing the cosmological horizon.