Simple math (the only kind I do) says a 584 rim sits 19mm lower than a 622 rim.
The first chart on this page shows a 21mm tire width increase required for a 584 wheel/tire to have the same height as a 622 wheel/tire:
So if your Pinarello truly maxes out at 25-622, you'd need almost 48-584 to not lower the bb at all. Not very likely to fit 48s. If you can fit 38-584, your bb should be about 12mm lower. Whether that's a problem or not depends on the bb drop measurement.
If you've got 42mm clearance at 300mm, and you're comfy with 5mm/side, 32-584 should fit between the stays. If you jump up to 38s, now you're down to only 3mm/side. With vertical drops and care, maybe doable. With horizontals I'd want a seriously locking rear qr skewer, like a DT RWS.
Keep in mind you've got potentially 7 potential pinch points on any frame: between chainstays, between seatstays, behind chainstay bridge, under brake/seatstay bridge, behind seat tube, under fork crown, between fork blades. About the only one I can't recall every experiencing is behind the chainstay bridge. I've met all the others.
So just knowing your chainstay clearance helps, but it's not the full story.
On all the vintage-ish/road-ish frames I've tried converting, I've found 10mm or so to be the max width advantage I've been able to get going to 650b, which would also imply lowering the bb 10mm or so. I'm not including touring/sport-tour frames that already cleared 32-622, or modern disc allroad/gravel/cross/yaddayaddayadda frames design to fit really wide tired of any flavor.
I think you're not going to know how it'll work without trying.
I'd start with measuring the bb drop. If it's 70mm or less, better chances. If >70mm, chances may not be as good.
Next step if you forge ahead is getting a 650b wheelset and a pair of 32-584s. If you want to stay around 32mm, use narrower rims. Wider rims might get you out to 34mm, depending on the tire.
Narrower 584mm tire choices are kinda limited, choices start opening up at 38mm & wider.
Conti makes the GP5k in a 28-584, maybe easier to find in Europe? I have a just-in-case pair, if I wind up with some lovely track frame with a 50mm bb drop that barely fits 19-622s. Not likely to ever get used.
At 32mm you've got the Hutchinson and the Grand Bois Cypres. I have the Cypres on my Raleigh, and I've used the Hutchinson in the past.
There's knobbies in 35-584, but not much in a road-ish tread. There was a Schwalbe Kojak slick in 35-584, but I don't see it on their website any more. Some retailers still have stock. 32mm road basically jumps to 38mm.
38mm gets you Rene Herse, Soma and others.
Don't forget to have fun!
Paul Brodek
Hillsdale, NJ USA