Facts:
PopCap released an official Bejeweled add-on in 2008 after a fan created a clone. (source) They followed it up with a Peggle add-on for World of Warcraft in early 2009. (source) These add-ons are notable because they use obfuscated code which is against Blizzard's UI Policy but an exception is made due to both companies closely working together. (source)
These are still available to download from PopCap's site right here. They are not being maintained but do work (with a few errors) in current WoW.
In 2009 (after the release of WoW Peggle) Blizzard hired PopCap's VP Greg Canessa. (source)
Blizzard started working on the Peacebloom vs Ghouls quest chain before contacting PopCap. They could have easily released it without any problems even if PopCap complained as it falls within fair use. PopCap loved it and had Laura Shigihara (PvZ's music composer and voice of the sunflower) to record "a few extra bits" for Blizzard to include. (source) This was later confirmed to be speech samples for the Singing Sunflower, presumably so that Blizzard could redistribute them at any time without needing to clear it with PopCap.
Even after the Electronic Arts buyout of PopCap, their official line is that things like this wouldn't change as PopCap is going to remain mostly autonomous sort of like Blizzard remains mostly autonomous from Activision. (source)
Speculation:
Quite honestly the Peacebloom vs Ghouls quest chain is fun the first time but it doesn't hold up to the real thing. I'm sure that if you had to do 15 stages of it in one sitting you would be quite tired of it. Plants vs Zombies on the other hand is something that you can play for hours and hours.
So really the only thing stopping you from doing this is that it didn't test well.