I'd say no, just to be safe.
While some folks say they have done it in different situations with success, I would tend to err on the side of safety and advise against it in your situation. I think all the discussion back and forth about the matter is more confusing than helpful to the OP. If you can find load data in a reputable published reloading manual using the LPP in your cartridges, I'd say go for it. In the absence of such data, I say better safe than sorry.
On a brighter note, it does seem that the LRP aren't in quite as high demand as other primers since stock has been seen running through several suppliers as of late. Just be patient and get some LRP when they are available.