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.