No

In Spanish, most of the words which come from the Greek "-ai-" (αι) go transliterated as "e". This fits better (though not exactly) the Greek pronunciation than leaving them "ai" in Spanish [*]. In Greek, like in English and French, "ai" is not "a+i" but a different sound. In Spanish, "ai" is "a+i". So while (Commonwealth) English can write "ae" and German can write "ä" (which comes from "ae") and pronounce it as a single vowel, Spanish cannot.

[*] Although "p(a)edophilia" is a scientific neologism, this happens also in the Greek words containing "ai" that passed to Spanish through a Classical or Medieval Latin phase as "ae", just as it usually does in the inherited Latin words with "ae".

Interestingly, though, "p(a)edophilia" is a historical exception to the rule. Whether the intention was to tell it apart from "pederasty/pederastia" (both in the sense of Greek boylove and the sense of homosexuality) or to avoid pronouncing the "pedo" beginning that sounds like "fart" (pedo), I don't know. Yet, the usual spelling and pronunciation used to be "paidofilia" instead of the more common transliteration of Greek "ai" as "e". Personally, I think that sounds better, but today that spelling and pronunciation is in decline and only used by pedants like I am when speaking about p(a)edophilia.

So, in conclusion, I think we can suggest "faiofilia" as a valid Spanish alternative (and implicitly endorse the "paidofilia" spelling of pedophilia too). Or of course, keep it simple and stay with "gerbillas" (gerbils, f.).