my question is grammatical: Is it correct that should can have the same meaning as if ?nil

While English does not have a conditional tense per se as do the Romance langugages, including French from which English is derived (among other languages), there are certain words that used to establish a conditional situation. 

In informal English, speakers and writers use the word if to begin clauses that are conditional. e.g. If this be true, we will not delay.  Along with the conjunction if, the subjunctive mood is used for the predicate [be is in subjunctive mood].  (This is why speakers say If I were you instead of if I was you)

Should  is a verb that is employed as a conjunction like if in this conditional tense, although it is not used as frequently as if, especially in America. This avoidance of its usage may be to avoid confusion since should is used used as an auxiliary verb to express necessity or obligation.  Here are examples that illustrate the difference between should as a conjunction (1), expressing a condition and should as an auxiliary verb in a sentence expressing necessity (2):

1. Should you move out, I will not be able to pay the rent on this apartment.


2. I think you should move out of this apartment.

Therefore, the short answer to your question of whether should can have the same meaning as if is yes, sometimes.