No, it's a lose/lose for both parties.
Why would MS split the profit from a subscription with Sony? You'll soon be able to subscribe to GamePass on mobile, any potato PC or touch-screen device, smart TVs with XCloud. It'll be easier than ever. Even with the inexpensive Series S.
Why would Sony allow Game Pass? MS always says they would allow Game Pass on a device if they can get the entire Xbox ecosystem on it (achievements, friends list, MS store). Essentially, if a PS user subscribed to Game Pass on PS5, and wanted to buy the game off it, would they go to the Xbox Store or the PS store? If they go to the Xbox store, Sony would get its third-party game sales on Game Pass cannibalized. If they go to the PS store... then what's the point of putting Game Pass there in the first place if MS won't get the money off the sale?
It's a lot of headache where neither two will ever agree on. In fact, Sony themselves are probably working on their own Game Pass competitor (like the PlayStation+ collection on PS5, which they will no doubt beef up in the future). There is zero chances they'd want a competing subscription service on their own platform.