I think it depends on how you market yourself, what position you're at and what the client expects and is willing to pay for.
If your clients are used to you doing odd jobs then they would probably not hesitate to ask you to do some illustration, whereas if you kept your jobs strictly in one area then they might not. If their budget allows for them to hire someone who 'specifically' does one area of design then they might do that, but if they are happy working with one person who covers multiple areas (jack of all...) then they might do that too, especially if they aren't looking for something that is going to require the absolute highest of standards.
And yeah, it definitely depends what it is, as Jimlad rightly says, if the job only requires small elements of illustration then fair enough, but if the entire job revolves around illustration then it might be better to outsource that job to someone else.