It is hazardous to ask questions about sound system of English without saying what dialects you mean, and what kind of analysis you are assuming, because the answer is "It depends...". The observable facts are "how things are pronounced", i.e. the phonetics of English, so you should start there. The vowel [ə] does not appear before [ɹ] (the English version of r) within the syllable, at least in most American dialects. Things get even more complicated and under-reported when you look at other dialects, so I will only talk about the main patterns of American English.
In words like "pervert" (noun or verb), "burn", there is a vowel-like thing in each syllable, which can be transcribed as [ɹ̩] (or [ɚ], also [ɝ]). Distributionally speaking, [ɹ̩] is in complementary distribution with [ə.ɹ], where [ɹ̩] occurs when the sequence is within a syllable, and [ə.ɹ] occurs when the vowel and consonant are in separate syllables (e.g. parade [pəɹɛɪd] – I'll come back to this form). A common phonemic analysis of [ɹ̩] is that it derives from əɹ, thus ɹ̩ is not an autonomous vowel, and derives from reduction of əɹ within the syllable.
Reduction is actually somewhat more general, since "parade" is also pronounced [pɹ̩ɛɪd] or [pɹ̩ɹɛɪd], that is, the "in the same syllable" condition is often dropped from the requirement of the reduction rule, and this is widespread, but dialect-dependent (it's a feature of more-western US dialects, though widespread throughout US English). The extended rule is optional, though very likely to happen (whereas phonetic [pəɹvəɹt] in American English is either extremely rare or unattested).
Cross-syllable reduction of əɹ can happen at the phrasal level, so that "a rabbit" can be realized as [ɹ̩ɹæbɪt]. This is much less likely, and this can lead to semi-minimal pairs like "a rest" [ə ɹɛst] vs. "arrest" [ɹ̩ɹɛst]. It is likely that if one were to extract examples of such words from a corpus of casual spoken English that there isn't really a difference between the two-word and one-word structures, but I don't believe a systematic study of this has been undertaken. An interesting and unanswered question is whether the more-casual form of "a rest" ever becomes phonetically indistinguishable from "arrest", or is there always some distinction.