It means will you support me?

The term "back up" in this context means support, like reinforcement, help, or assistant if anything goes wrong. So you could say "Will you back me up?" for a fight for instance. It could also be used for asking someone on a date, like moral support. In that case, being a back-up for someone who is about to ask someone on a date is being there to help encourage them to follow through with it.

you will be my alternate *in case something goes wrong*

it means you will be my successor .?