Is frequency analysis a useful tool against encryption by multiplication? If I transform natural plaintext by:


making each letter two decimal digits, considering the whole as a decimal number;
multiplying by the key (some integer constant), giving the ciphertext;


would frequency analysis still work?

Exemple:

Plaintext:     G o l d U n d e r S e a
Number:       071512042114040518190501 x 911
Ciphertext: 65147470365890912071546411


To get the text again simply divide by 911. Conversion of the ciphertext to letters could be added somehow.

Assuming frequency analysis is not an option, how would one break this?

Note: The question has been improved by the OP, then re-tagged and further edited for clarity. I now wish I could rescind my own vote to close it.
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.