Yes. Even among speakers of Received Pronunciation, /eə/ is sometimes realised as [ɛ:].
In fact, some dictionaries (notably, newer Oxford dictionaries) transcribe it /ɛ:/, as Lexico does here. (Other dictionaries use /eə/; Wiktionary's /ɛə/ seems less usual.)
Phonetician John Wells comments on the rival transcriptions (and variation in pronunciation) as follows, referring to /eə/ as the "standard symbol", and /ɛ:/ as a "long monophthong":
People do increasingly use a long monophthong for this vowel, rather
than the schwa-tending diphthong implied by the standard symbol. What
used to be a local-accent feature has become part of the mainstream.
There are millions of English people, however, who still use a
diphthong. To produce the distinction in pairs such as shed -- shared
EFL learners generally find it easier to make the square vowel
diphthongal ([eə]) rather than to rely on length alone.
(Lexico has "shed" as /ʃɛd/, and "shared" as /ʃɛːd/ - a length-based contrast. Wells' point is that it may be easier for learners not to rely solely on length to make the phonemic contrast. The "standard system", on the other hand, transcribes "shed" as /ʃed/, and "shared" as /ʃeəd/.)
To pronounce it [ɛ] or [e] without elongating it - using the "e" of "shed" for the first vowel of "various" without lengthening - would be less normal in RP, and might be noticed, but wouldn't affect comprehension. (If you did it in a word like "shared", it could affect comprehension, though context is usually a big help to the listener.)