Is frequency analysis a useful tool against encryption by multiplication?
Frequency analysis would work on average quite poorly on ciphertext of the proposed cipher. How exactly depends a lot on the value of the key: for some weak keys likes 1, 3, 30, 30000.. it works essentially as well as for any mono-alphabetic cipher. For 103, it still works well. For any key, given enough (lots of) ciphertext, it could still distinguish the ciphertext from random.

Frequency analysis is NOT the right tool to attack the proposed cipher. It is much easier to find the key $k=911$ by trying small factors $k$ of $c=65147470365890912071546411$ (in ascending order) and keeping the one (or those very few) such that $c/k$ has all digits in its base-100 form in range $[1\dots26]$. That attack would not work well for a huge key purposely constructed as the product of many small factors. However, I guess refinements are possible.

An even more devastating problem occurs when a key is reused for different ciphertexts: we can compute the GCD of the ciphertexts, that will be a multiple of the key, and the key itself with few ciphertexts (sometime 2 or 3, growing only slightly with size of the parameters).

Therefore, the cipher is weak and has no practical interest.