Yes, but scoring should be based off tips, to keep it authentic
Calling it pole dancing alone would be a hard sell.
Maybe easier to get this be made into some kind of routine in Gymnastics instead. Like the parallel bars or what ever else is done in Gymnastics.
Synchronised spinning?
Where I live, they call it “pole sport” to mark the difference with the dancing (also called “pole exotic”)
Source: I train pole sport
Vertical bar?
If you start thinking deeply enough about any competitive sport then the whole idea is bonkers, so it doesn't really need any justification in my mind. Anything that requires skill and is competitive could be in the Olympics. I can't stand the whole thing anyway. Take it back to amateur hour and then it'd be interesting. Maybe select the competitors for each country randomly on application, that'd be a laugh.
I can see this genuinely happening after skateboarding and breakdancing of all things.