Many web teams may consider it a forgone conclusion that you should redesign your site as part of your migration to a new CMS.  But it doesn't necessarily have to be that way.  In fact, there are many disadvantages to doing a redesign and migration at the same time.

What's the case for doing both at the same time?

• If you can't separate redesign from migration
• Budgeting ease
• Easier to sell internally
• General bandage removal approach (rip off the bandage all at once so the pain passes quickly)
• Potentially avoid doing some work twice
• Organizationally can't manage a program lasting longer (at least in the "best case" with nothing going wrong)
• If redesign is an extremely minor component, so separating would be forced

So, why consider separating migration from design?

• Fundamentally, to limit what needs to happen at the same time -- reducing significant project risk
• It always takes time to understand your requirements, and a redesign throws in more requirements that need to be understood -- separation means the various stakeholders can more easily be on the same page about what needs to happen and whether the site is working as it should
• Probably higher quality at the end
• Results sooner
• Can separate out different decisions
• Reduce chances of the entire project grinding to a halt

Ideally you could find a practical middle ground, such as minor (but high impact) redesign changes while undertaking a major CMS replatform.  I believe a deep redesign during a complex implementation / migration presents high risks. 

Hopefully the factors above can help you make the right decision for your organization.