KarriS
AFAIK the whole roomfinder "window" is brought in via a Webview component, so technically it has zero to do with the desktop client, it is just shown within Outlook. Therefore I would suggest it should be the same with OWA.
As to the long replication times for changes: I was told, that this is due to two factors
a) some cloud size tasks around room finder are running just once every day, so it can take up to 23:59 hours till your changes are actually being touched.
b) some Outlook side parts are also only running during logon/startup and afterwards once per 24 hours. Quite similar to the way GALs (global address lists) are handled. (BTW Because of the above webview part I assume this is only valid for when not opening the room finder but just choose from the suggested rooms, which seem to be cached locally)
However, according to my experiments, powershell queries against Exchange Online report back only after a few minutes. So at least you can double check if your changes have been entered correctly, but your users still have to wait way too long.
We all agree with you.