Can the dialectical final "ue" be written in pinyin "ue"? The final ue can be found in some Chinese dialects/topolects. It seems to also be written properly as uɛ if I'm not mistaken.
The Wikipedia page for Sichuanese Mandarin lists an example:

uɛ
ue
国

Which I would understand could be written, in full, as gue without any sort of tone markings.
Does ue/uɛ just equate to pinyin ue?
Hanyu Pinyin is generally used for Standard Chinese. If you want to represent /uɛ/ in something consistent with Hanyu Pinyin, you could use uê. The Wikipedia article was using Sichuanese Pinyin, which may not be compatible with Hanyu Pinyin.