Welcome @Boiledcabbages and I like your username!
Great choice
You are talking about two magnets, so yes, but, it could also repel (I assume the stirrer is axially poled also)
What continent / city do you live in?
The reason I ask, is, if you are willing to send a stir bar, I’m sure somebody here would be willing to test it for you…
You could do this if you had a 
with you and magnetised it etc.
here is a specific post, but the whole thread may be of interest.
We also have a few rock climbers here, but I can’t think of one offhand with a fingertip install.
Hopefully, somebody can answer this for you.
It is not
Not even close to some of the posts we have here