A hot toddy can get you drunk if you drink too many of the hot toddies.
However since the hot toddy is mostly drank in small quantities then you will likely not get drunk from the hot toddy.
I have a hot toddy every now and then and especially when I have a cold or flu virus and never have gotten drunk off the hot toddy.
Just drink the hot toddy in moderation and you should never get drunk from it.
But just like all alcohol when you drink it in excess the hot toddy can get you drunk.
Drinking some alcohol can be healthy in moderation but drinking too much alcohol can lead to alcohol poisoning and even death.