As a yes or no, then yes, phosphorus poisons catalysts. But it depends on oil consumption, type of phosphorus, amount of precious metal loading on the catalyst, the rest of the oil formulation, and many other variables. Even with those factors, the life of a catalyst with "older oils" was ~80,000 miles.
Newer cars require even longer catalyst life, and although I have not kept up with this, I think it's safe to say that they must now meet the equivalent of 120,000 miles of service (not perfection, just service.) I find that since the OEMs have not come up with an engine test that predicts an oils effect on catalysts a black eye for them. They have continually said phosphorus is "bad" but the limitation has always been a number picked by them. There is no magic to the levels used; back during API SG, SH it was around 0.12 wt%, then was reduced to 0.10 wt%, and is now at 0.08 wt%. The next oil category that will be introduced next year will be not more than 0.08 wt% and not less than 0.06 wt%. I'm bothered because it does not allow the lubricant formulators to build up to a performance target; they are technically handcuffed to a numerical limit.
Gasoline (premixed charge) engines emit relatively more HC and CO than diesel engines, which emit more soot and NOx. Therefore a diesel engine's first line of exhaust treatment is a particulate trap. Without the precious metal concern, diesel oils can retain the previous normal level of phosphorus. However, the particulate filters trap other things besides soot, such as sulfur (from the fuel), sulfated ash (a measure of detergents in the oil), and also phosphorus (from oil consumption). In time, the phosphorus level in diesel oils may also decrease even though it is not targeted directly.
There are now a few break-in oils by Joe Gibbs, RP, etc. If you are building a flat tappet engine you will need this. It's not a luxury, it is a requirement, since an off-the-shelf oil is probably not good enough. Builders have also used diesel oils successfully and motorcycle oils should also be good (since many stayed at API SG performance due to the newer oils incorporating friction modifiers.) European oils of higher viscosity grades (those that don't try to be fuel economy oils) would also be acceptable.
OEMs want fuel efficient, catalyst friendly oils in the 10W30 and lower viscosity grades. It's another reason 0W40, 5W40, etc oils will be able to still have normal phosphorus levels.