To a first order approximation. There's a bit more to it than that, so don't commit to 44-584 if 25-622 is within 1mm of interference. You really need to account for rim width and tread band thickness to get a proper estimate.
Ta. It looks like there aren't a lot of ~44c tyres anyway so I might just go down to 34c and eat the loss of clearance (running 165mm cranks so shouldn't be the end of the world).
Edit: for "a lot" read "within a reasonable budget for the build I'm considering"
To a first order approximation. There's a bit more to it than that, so don't commit to 44-584 if 25-622 is within 1mm of interference. You really need to account for rim width and tread band thickness to get a proper estimate.