You could if you suspected that there might be a poster with multiple accounts - which is against the forum rules. You'd likely get a response from the Supermods that the IP checker tool on the forum hasn't worked since the site's owner switched the IT platform on which the sirte is based - so largely a waste of time and effort.
In addition, if someone actually has the inclination to register duplicate accounts using overseas servers or VPN variants then it is easy to do - so requesting an IP check as a means of it being 'absolute proof' of where someone posted from - as HIAG did - is a complete nonsense - proving nothing one way or another. HIAG was aware of all of this but demanded that the Supermods made the IP addresses public in any case - had very little to do with him proving that he had been on holiday in Las Vegas - but everything to do with him wanting to show that posting histories for him and Saints would throw up a different IP addresses - even though it couldn't possibly prove, one way .or another, whether or not HIAG was actually sitting in a room anywhere in the world using two different devices

... complete farcical bollox which backfired spectacularly in the end