Yes, definitely mention that the writer suggested you send the story to that editor. The story will still have to speak for itself, but such a referral can get a story past a first reader, or to the pile set aside for a later, more careful reading.
Do not kid yourself for a second about "fair chance". There's a good chance every submitted story gets read, but that's where the fair chance stops. A good referral will get your story read faster, and will get your story past the first readers at many publications. It will also mean the editor will start reading with high hopes, rather than with the very low hopes that usually come from reading general slush.
It may have been Kristine Kathryn Rusch who wrote about three levels of slush. Level one is all the famous writers out thee, the geniuses who always write a great story. They go in one pile. This does no mean the editor will automatically buy all those stories, but she knows they will all be good, worthwhile read.
Level two is writers the editor may have heard of, that have been published here and there, that may have sent her good stories in the past, even if they weren't quite good enough to buy. These are the writers who show serious promise.
Level three is everyone else.
Anything you can do to get yourself out of the "everyone else" stack and into the writers with promise stack is a good thing. If I see a referral like that, which really isn't a referral at all, just a suggestion of where to send the story, with the implied thought that it is good enough to send, that story goes into the second category, which means it will be set aside for a closer read.
"Good luck" is meaningless. When a pro writer reads a story, tells you to submit, and says where, you're an ijut of you don't mention this in a cover letter. It's one of those things that won't sell the story, but almost certainly will get it read faster, and with a better frame of mind.