I don't see anything wrong with this sentence: It will be greatly appreciated if the bill is paid by check when possible.

You're right; there's nothing wrong with this sentence. But you can make it much better by putting it in the active and not passive voice. We would appreciate it if you paid the bill by check.

if you pay the bill?

The "if" clause usually follows "appreciate it." If that's confusing for you, we can change it to
Please pay the bill by check.

Which one are you saying is correct?
We would appreciate it if you paid the bill by check?
We would appreciate it if you PAY the bill by check.

We WOULD appreciate if you PAID the bill by check.

or

We WILL appreciate it if you PAY the bill by check.

The correct phrasing would be "We would appreciate it if you paid the bill by check." In this sentence, "would" is used to indicate a hypothetical or polite request, and "paid" is in the past tense to match the verb tense of "appreciate."