Is it correct to say "이거는 사괍니다?
It is correct, though I think it's less common in writing. The root "-이-" if the copula is frequently omitted after a vowel, though exactly how often depends on what follows after that. E.g.,
저것은 책이다 / 저것은 학교다 (OK) / 저것은 학교이다 (OK?)
저게 책이냐? / 저게 학교냐? (OK) / 저게 학교이냐? (weird)
In both case, "학교이다" and especially "학교이냐" sound less natural to me. So, in the same vein, "사과입니다" can become "사괍니다" - however, unlike the examples above, in this case I think "사과입니다" is considered "better", especially when writing.
Also there are cases where -이- cannot be omitted at all, even after a vowel:
일등인 사람 / 둘째인 사람 (OK) / 둘짼 사람 (X: can only mean "둘째는 사람이다")