Vocaloid and UTAU culture thrives on something that I've called the Unspoken Doujinshi Agreement. Applied to fanworks of things like anime, it's a sort of tacit agreement that many anime/game/whatever companies have with doujin artists in Japan that they will turn a blind eye to the technical copyright infringement as long as the artists continue to support and promote the original work. The difference in this case is that we're dealing with indie producers, not with corporations.
So what do you do in this situation? Honestly speaking, if you had to ask every single producer for permission to cover or do anything based off their work, this community would be a lot smaller - a lot of people, Japanese or otherwise, probably would feel a little intimidated having to ask every time they wanted to cover something (and I'm sure ryo of supercell would have tons of emails in his inbox a day). It's something that the community understands is unintuitive and impractical. Even on the legal end, if you wanted to boil down to it, technically every cover of any song by DECO*27/sasakure.UK/any producer under U/M/A/A or other label would be illegal as well. They allow it because they understand that this is one of the base requirements for the culture to subsist on, and many of the producers in question like it anyway.
See, the thing is, when producers in this community release off vocals, they're not blind. They know people are going to take that as a tacit invitation to cover their song, on the internet or not, unless they post up a corresponding note "do not publicly post covers on the Internet". And although perhaps it's getting into analytical psychology, I know for sure that if I, as a producer, really didn't want people to publicly post the song, I would absolutely attach a ToS or statement with it. Besides, the idea that off vocals are included for people to listen to the BGM is a little silly because...honestly, most songs are made to have the vocals with them, so (although some producers may disagree with me) releasing an off vocal for people to listen to for fun is basically like releasing an incomplete product. It's like releasing a video game with all the sprites removed so people can appreciate the backgrounds.
In the case of Aimai Elegy, do note that DECO*27 intended that song to be an album special song, sung by marina, and that he never released an official off vocal for it. It stands to reason that he wouldn't want covers of that song, and generally speaking most people understand that when they see a Vocaloid producer make an album-exclusive song, you don't just make a fanmade off vocal and cover it. (The issue of whether it's okay to cover songs if DECO*27 personally just dislikes covers - and mind you, this is the first time I have ever heard this claim, although I'm not necessarily doubting it - is something that I think each person should personally decide for themselves, and not concern themselves with trying to analyze people's psychology. Has anyone ever bothered asking DECO*27 about this personally anytime recently?)
Knowing the climate in the community, on Nico Nico Douga or on YouTube, I think you should feel free to cover if you see an off vocal released. Of course, you shouldn't try to make money, and you shouldn't be publicly distributing off vocals that come only on albums, and if you really feel nervous about it there's no harm in dropping an email to a producer like ____さんの曲「_____」のカバーを作ってもいいですか? or something. But I don't think there's some kind of cultural taboo in doing this (no, seriously, I dare you to claim to me that all or even most of the UTAU, Vocaloid, or utaite covers on Nico Nico Douga were all made after individual emails to the producer to ask for permission). Considering that Vocaloid culture's been around since 2008, if people covering things without permission were really that much of an issue, you'd think there'd be some action taken against it by now. Of course, if an individual producer says that they want people to stop covering songs, then by all means you should stop and respect that. I think the community has been very good about that so far.