It should leak, yes. Use the replacement glass while you are waiting on your order. Otherwise you will just be wasting juice and exposing your mod to the possibility of a leak.
Best of luck, McGuyvering may work under certain circumstances, but probably not in this one.
I also kind of go "ewww" any time my tank breaks or cracks and I just worry about glass pieces. It's not really a "logical" worry, you aren't, in all likelihood going to be inhaling glass shards (probably) but I just.... the idea of using a cracked tank is so unappealing, in so many ways.
When you can afford it, a backup, then a backup for your backup.
Best of luck though I hope you get it resolved soon.
Anna