This is often missinterpreted. A high K does not imply the same behavior as SHAKE does, because they are applied at different times in the MD cycle. SHAKE's most useful benefit is an increased timestep for the entire MD simulation. Usually a 2fs timestep can be used in all-atom simulations from just constraining the hydrogen's bonds. So BEFORE the force evaluation and motion integration takes place, the hydrogens are brough back to their ideal distance. But in contrast to SHAKE which is applied BEFORE force and motion computation, a high K value for the bond would only be effective AFTER the motion already took place and would result in an enourmous force at the NEXT timestep. So the higher the timestep, the large the displacement of an atom and therefore the higher the force and resulting velocity at the NEXT timestep, causing an escalation of the hydrogens and instability of the simulation.

To come back to your question, if your cg bead is so lightweighted that it limites the usable timestep for the rest of the simulation cell, a high K value for the bond will most likely not solve your problem.

As Norman mentioned correctly, using SHAKE algorithm and assigning a great value for bond constants do not behave the same. Assigning great value for bond constants is just acceptable during the minimization procedure where the SHAKE is not allowed.