I'm going to provide an answer based on my experience and obligations as a Professional Engineer (PE), which is generally similar to the obligations of an Registered Architect (RA).
You do not state exactly what is meant by 'things go seriously wrong with the project,' but in general it doesn't matter. What truly matters is that Alice is the Registered Architect and Belle is not; this is reflected in the billings whereby Alice is charging $200 an hour and Belle is $100 an hour. The fact that things have gone seriously wrong with the project is now Alice's fault. Even if the fault is in an error that Belle made, it is still Alice's fault because of their obligation of 'Responsible Charge'.
In NJ, the definition for Responsible Charge is detailed in Chapter 13:27 for RAs and 13:40 for PEs, but is generally the same to mean that the professional in responsible charge shall provide effective supervision over all aspects of the work.
Would the misrepresentation be considered to be "material"?
Probably not unless either the contract provided a clear definition on what is meant by the term 'architect' or there is relevant law that defines what that term is and how it may be used within business. In NJ, there is a definition for 'Engineer', but it's only applicable within the bounds of Chapter 13:40 and is not intended to limit how the word might be used throughout the State. As a whole, someone operating a train can still call themselves an 'Engineer'.
Furthermore, we use the term to describe lots of different people within the engineering profession. For example, you might see billings for Engineer I, Engineer II, Engineer III, Engineer IV, etc. all attempting to provide more diverse billing structures to make hourly rates match experience levels.
Furthermore, there are plenty of times in the United States as a whole, where someone might be fully registered and licensed in one state but not another.
Would Conrad have to prove that he would not have entered into the
contract if he had known that Belle was not an architect?
It's likely not relevant. As I described above, there are a litany of reasons why both could be described as an Architect, but what truly matters is that one of them is a Registered Architect and thus has responsible charge over the issuance of plans.
Does Conrad have to show that the standard of work from Belle was not
the standard of work that would have come from an architect?
No. Alice is the Registered Architect who signed the plans. The standard of work by Belle is by default the standard of work of Alice whom has responsible charge. If Alice has issued plans that are fundamentally flawed, the error is their fault.
Conrad does not doubt that the hours attributed to Belle are honestly
attributed, but is it material that the work is shown as having been
done by "Belle (Architect)"?
As a matter of resolution for this, I can say that you're more likely to get something done in a cost-effective manner by raising a complaint with Alice than anyone else.
To exemplify, a few years back a friend of mine had hired an architect to design a building addition for their home. The architect's scope of work included completing a survey of the existing structure so they could base their design upon it. During construction, it was revealed partway through that the proposed expansion was going to conflict with the existing windows on the second floor.
This is not acceptable for a litany of reasons, but it should've been discovered in design, not construction. Reviewing this issue with my friends, I encouraged my friends to document the issue in detail, meet with the Registered Architect on-site, and demand a solution.
Thankfully, this went well and the RA accepted fault for the error. The costs of revising plans and additional construction costs was simply borne by the RA.
Had the RA refused to accept fault, the next alternative would've been to make a claim against the RA's insurance carrier for Errors and Omissions. E&O insurance is stupidly expensive, but also absolutely necessary for an RA to operate. It's often much cheaper to just pay the cost of plan revisions and construction change orders than to have a lot of claims on your E&O.