I think some of your basic assumptions might be incorrect. It does not appear that Readonly is a core module, and it appears that you have the syntax for its usage wrong. From what I'm seeing, Readonly allows you to set a normal, sigil-bearing variable to read only, and use it in the standard manner. By comparison, constant gives you a bareword constant that you can't use in all the same contexts as a normal variable (e.g. stringwise evaluation of scalars). So it my mind, it boils down to the following tradeoff:

Is the cost of installing the CPAN module outweighed by the utility of being able to use the value more conveniently?

And that's really something you need to answer for yourself.

Update: for future reference, you can see what modules are included in the standard perl distribution by reading perlmodlib. And you can also find what version a certain module became core with the help of Module::CoreList.