Is it valid to argue that magnets might appear to be effective if the sample sizes are larger?

Yes, it;s a valid argument.
Especially in medical field. The treatment with magnet is used to reduce the pain that patients experience in their joint (mostly used in treating backpain).
Since the effect of the magnet is to reduce pain, the patients will feel much more relieved if the magnets force are greater, which give the impression that large magnet is more effective compared to smaller ones.

Pilgrims is the answer