Can depression cause problems with language?
Depression in can cause poor concentration, inability to speak in normal, fluent tones and rhythms. A person may speak (and move) extremely slowly and have trouble putting thoughts into words.
In elderly person depression may even produce a picture of mild symptoms of dementia, that improve when depression is treated. These scenarios could be what you mean in terms of problems with language.
However, if the person does not have problems with moood, appetite, sleep, energy, concentration, etc., then I would look to other brain disorders to explain problems using language or communicating clearly.