Should I mention being enrolled in distance course currently as a backup option in application form? I am currently enrolled in a distance masters's course in my country as a backup. I will be only applying to some really very competitive schools. If I don't make it through those schools I will apply next year or year after that and continue to do so till I make it in. I am very very passionate about these schools and the research going on in there.

Class for this distance course will begin by the end of this month and I will quit as soon as I get an admit in any school of my choice. Should I mention joining the course in my application forms? 

Some of these schools want me to upload transcripts of any course I have attended after school. Considering the fact that the course has not yet begun there is no way I could get a transcript from them.
The basic rule of thumb is this: if you're actively involved in something at the time of application, then you should mention it. If you're tentatively enrolled (for example, you've been offered admission, but have not yet officially registered), then it doesn't actually count, and you need not mention it.