Not including Unicode would not make it unable to process Unicode, since you can implement whatever character encodings you want to do, without being stopped by the programming language's bad idea of character sets.
However, processing Unicode is often unnecessary anyways. Sometimes you only need to deal with ASCII (and can pass through non-ASCII unaffected). Sometimes the Unicode handling can lead to bugs (and sometimes can be security problems; and this is not usually due to Unicode being implemented incorrectly). Unicode can also make the code less efficient especially when Unicode is unnecessary but sometimes even if you do deal with Unicode (due to internal conversions and counting and other stuff it is doing when it is not helpful or might even be against what you are trying to do). Inherent Unicode handling can also sometimes make it difficult to handle byte strings especially if they do not have many of the same operations available to them.
It also tends to lead to bad design (API design and programming language core design). Sometimes it is used even though byte strings would be more appropriate, or sometimes you might want a separate "file path" string type (I think Common Lisp does this). Treating source files as Unicode text can also be probematic.
Unicode is not a very good character set anyways; it is bad in many ways. I could say what ways it can be bad for many different languages and for other purposes such as security and efficiency and accessibility, too. (Some people say it is better than dealing with other character encodings for multilingual text. I have worked with it and found the opposite to be true.)
However, processing Unicode is often unnecessary anyways. Sometimes you only need to deal with ASCII (and can pass through non-ASCII unaffected). Sometimes the Unicode handling can lead to bugs (and sometimes can be security problems; and this is not usually due to Unicode being implemented incorrectly). Unicode can also make the code less efficient especially when Unicode is unnecessary but sometimes even if you do deal with Unicode (due to internal conversions and counting and other stuff it is doing when it is not helpful or might even be against what you are trying to do). Inherent Unicode handling can also sometimes make it difficult to handle byte strings especially if they do not have many of the same operations available to them.
It also tends to lead to bad design (API design and programming language core design). Sometimes it is used even though byte strings would be more appropriate, or sometimes you might want a separate "file path" string type (I think Common Lisp does this). Treating source files as Unicode text can also be probematic.
Unicode is not a very good character set anyways; it is bad in many ways. I could say what ways it can be bad for many different languages and for other purposes such as security and efficiency and accessibility, too. (Some people say it is better than dealing with other character encodings for multilingual text. I have worked with it and found the opposite to be true.)