No.
Look around you. Are you working at Microsoft? If so, are you working on .NET itself? Congratulations, your assembly may actually be justified going into the GAC. If you answered No to either of these questions it’s highly unlikely that your assembly is going to be sufficiently widely used that software using it will assume its presence rather than include it with its own binaries.
The benefits of installing into the GAC in the general case are relatively small and doing so incurs additional complexity. It also prevents scenarios such as allowing your application to be dropped into a directory and run without installation. Just say no.