Sometimes, but not always the case. There is actually a bug that makes it so that the vends stay open even after everything has been sold. I've looked at the bot coding and there isn't anything which makes it stay open after everything has been sold. In fact, most of the vend bots will automatically go and restock once empty, or completely just disconnect and log off once empty.
Also not a every bot will do the "pricing high" to leave shop open, a lot of players do this as well for various reasons. To market their shop name, to be humorous, sheer boredom, etc.
I find that majority of the time, vendors that are reported with their shops open, pass bot check