I'm wondering if the diminished diatonic chord (iio) in the minor scale functions as it does in the major scale, where it's not used as often as the other six diatonic chords?
Yes it is used. Depending on what period of music you want to talk about, it's more or less common. For example, in classical pieces you wouldn't see VII that much and when it's used it's not functioning as VII, but as a point of modulation to the relative major. v is also rare as typically V is used instead to make use of the leading tone.
In general when talking about harmony the more relevant question is not how often a chord is used, but how is it used as part of a progression so the rest of this answer will focus on that.
In classical music, you may see it as a predominant used to add extra tension. When it's used you'll typically see it in first inversion to keep a tension out of the bass so you may see the progression ii6 - V7 - i. A very similar progression that takes this to the next level with chromatizim is using the Neopalitan chord which is the same progression with the root of ii lowered. This would be analyzed as N6 - V7 - i.
In jazz ii7 - V7 - IMaj7 is pretty common, when the key is minor iiø - V7 - IMaj7 (Dø G7 Cmaj7) is also common. You may also see it as part of a tritone subsititution like iiø - tt - IMaj7 (Dø Db7 Cmaj7).
In today's popular music you won't see iio, but you will see ii a lot in minor keys especially in genres that use power chords like metal and punk. When you do see as a diminished chord (or power chord with lowered 5th) it's typically heading to i or III and just used in passing.
This answer does not touch on the full scope of minor harmony. I highly recommend you go over the questions on the site that are geared toward that so you can start understanding minor harmony better.