yes.

"Yours sincerely", or just "sincerely" is completely appropriate in that context and is actually more common than "faithfully"

The standard rule in BE is that letters beginning "Dear Sir / Madam" must be signed off "Yours faithfully", never "Yours sincerely". This is what I was taught in school back in the 1980's.

However, the convention is disregarded as often as it's observed.

Agree with Steve. In my opinion the rule still applies in formal business letters, at least we still apply it in the translation agency I work for, but we use British English. I think this might be another AE/BE issue.

In AE style it doesn't matter whether you know the person's name, but in (traditional) BE style it does.

AE:

Dear Mr./Ms. X:
Dear personnel manager:

Sincerely,
Sincerely yours,


BE:

Dear Mr/Ms X:

Yours sincerely,



Dear Sir or Madam:

Yours faithfully,


Of course you can break the rule, but if you're taking a test on the format of a business letter, it would be better not to. (-: