Does this mean it will not function as is unless I migrate?
Correct, at some point heroku will remove support for the bamboo stack completely. Since Rhosync doesn't support ruby 1.9 it cannot run on the cedar stack so you will need to migrate. Note that Rhosync has not been actively developed for quite some time so if you're developing/maintaining a Rhosync application it really makes sense to migrate to Rhoconnect as soon as possible.
So, if I am to follow those migration steps, does it mean I'll have to first clone it to my dev machine, follow the steps and then push it back?
Yes, RhoHub only supports the git interface for pushing/pulling code now.
OK, thanks, things are much clearer now