The dll mentioned in this thread is good, but I don't want to have to distribute that to everyone's machines, so I came up with an alternative. The script that follows would check OneDrive for a folder called Documents and returns its status.
# ID 303 = "Availability status" | The status is generally one of the following...
# "Always available on this device", "Available on this device", "Available when online"
$OneDriveDocs = "$env:OneDrive\Documents"
$Shell = (New-Object -ComObject Shell.Application).NameSpace((Split-Path $OneDriveDocs))
$Status = $Shell.getDetailsOf($Shell.ParseName((Split-Path $OneDriveDocs -Leaf)),303)