Short answer: yes. Shooting separate (or dual-system) sound is generally a good idea, especially if you're shooting film-style and can afford the extra crew and equipment.
You'll end up with two recordings of the same take—a primary (on DAT) and a backup (on Mini DV). Besides providing protection against data loss, having two versions of the soundtrack is a very good idea for technical reasons.
Like meticulous lighting, dual-system audio is a film-style technique, and the only reason not to do it is that it involves additional time and expense—luxuries you may not have on a news-style shoot.
Even though consumer and professional DV recording formats ...