No, your app will continue to work with V1 (for now).
You cannot get a new V1 license (old news, right, not since early 2013), but your current license is still valid.
At some point in the future, Google will likely decide to cut access to V1 - that is why they deprecated it, and that is why they have given us all plenty of warning.
Basically, we all "should" have started working with V2 in our new apps months ago, and by the time they choose to shut down V1, we "should" all be in a position to upgrade our old apps.
("should" i.e. in theory.... in practice, well, maybe not all of us are with V2 yet)