It is not just that some birds migrate during the day, but also that many birds make similar calls during the day and at night. For example, a local nocmigger picked up the call of a Yellow-browed Warbler at night, which I understand was the same sound as you would expected from an autumn waif during the daytime - the foraging contact call, therefore seems to be the same as the night-time migration (contact?) call.
Oldbird.org, were probably 'the pioneers' or nocmigging, and their CD of North American landbirds includes copious examples of bird calls that are split into daytime and night-time recordings, with the purpose of showing that sonograms of the two are often the same. As a UK example, many birders are very familiar with the daytime calls of Redwings and have no trouble picking out the calls of migrant Redwings at night. For some species we need to focus on daytime flight calls, which can be distinct from calls of perched birds.
Some of the recordings on the Oldbird.org CD are of late migrants at daybreak - e.g. Swainson's Thrush 'dropping out' of migration at dawn. This would be another way of determining what a bird probably sounds like during migration. I think however, this is an easier trick to perform in places with heavy migration - at Cape May, I have been stunned by the sheer number of birds dropping out of the sky at dawn on the right autumn day. Whereas, I suspect that where I bird in the UK, it could be rather hit and miss.
I am not sure how much things have changed recently, but there are some species where we simply do not know if they have a nocturnal migration call. For instance, Oldbird.org stated a long time ago, that Northern Wheatear's have no known nocturnal call. Obviously I have heard Northern Wheatear's alarm call and sing, but otherwise they seem rather silent to me. I can't recall ever reading that anyone has picked up this this rather common migrant during nocmigging, so perhaps they have no call, or perhaps we simply don't have a daytime equivalent in order to work it out.
I suspect that with nocmigging you probably have to be a bit ruthless - there will be plenty of recordings that are either poor quality or unrecognizable (or both), and I am not sure of the value of uploading such recordings to Xeno Canto. It is probably best to recognize that there will be an element of 'chaff' you cannot do much with. But if you have a clear and distinctive call, that you don't recognize, then the collective power of the Xeno Canto users is definitely worth a try.
