What effect does river channelization have on the surrounding water table?
The concept of rivers being the outcrop of an aquifer at the surface is a useful generalization, but tends to simplify the real world.

The water level in a river can be higher than the water table in an aquifer. We would describe the river as 'losing' water and it would recharge the aquifer. So in that case channelization would reduce aquifer recharge and potentially lower the water table. As an example irrigation canals in arid areas are often quite leaky. Projects to line the canals to reduce leakage have frequently had the unintended consequence of cutting off local recharge to aquifers used by farmers adjacent to the canal.

If the water level in the aquifer is higher than the river we describe it as a 'gaining' river. Channelization would reduce river flow and lead to higher water tables in the aquifer. The consequence of the higher water tables might be increased spring or river flow in another part of the aquifer - or in the worst case emergence of water adjacent to the channelized section waterlogging the ground. The extreme case of filling up a whole region is improbable, as once levels rise enough the water will just flow back into the channel, or further rise will be balanced by evaporation from open water.

Stretches of river may change from losing to gaining, and vice versa, seasonally, or in response to changes in geology or topography over quite short distances. Natural river beds are often not seamlessly connected to the aquifers they run over; muds and silts on the river bed can reduce permeability and effectively cause natural channelization. Equally artificial channelization is rarely 100% effective and leak proof.