Why would you want to do that?
In theory, yes. In practice, it would be tough and impractical. Say you went to MK from 9 - 12 noon, then to Epcot. The fastpassses you got at MK would probably be for sometime in the afternoon. When you go to Epcot, it's likely that you'd get fastpasses for an evening time, if there were fastpasses left. So, youcould PROBABLY use the MK later than the posted time, and you might be able to still get fastpasses for Epcot (I'm thinking Test Track, maybe Soarin')
So then you have to ride both of those using your fastpass, and still have enough time to get back to MK, and use your fastpasses before park close. IF it's one of the times where MK is open until midnight, then you could probably make it work, but if it's one of the nights where MK closes at 7pm...
But my real question is why? Why not do everything you want at MK, and THEN go to Epcot for the rest of the day. f it's just for the idea of having FP's for two parks, I'd say it isn't worth the travel time.
With lots of days, the price of park tickets goes down, but I still really like to think of a park ticket being worth about $50. Then you have to figure how many hours in the park you're getting for that $50. At five hours, you're paying $10/hour to be there (not counting food, lodging, and other expenses) If you look at the big picture - let's say your spending about $1050 per person for six days at Disney (and that's a fairly lowball estimate: $200 air, $300 room, $50/day food, $250 park ticket w/hop). Let's say your awake for 17 hours a day (sleeping 7 hrs per day)- then you're paying about $10 per AWAKE hour to be at WDW. If I've only got 10 -12 hours to be in the parks each day, I'd generally rather not lose two of those hours of park time in transit.
Beyond that , you're gambling that Epcot will still have fatpasses to give out. What are the fastpass attractions at Epcot anyhow - TT, M:S, and Maelstrom? Couldn't you just hit those three without fastpasses in your afternoon? Or maybe one FP for TT, and wait in line for the rest?
Having said all that, there was a day, a few years ago, where we went to MGM in the am, then went to Epcot until park close. It was 9:30, everyone was still excited, and MK was open until midnight (Easter week). So that night we hightailed it over to MK to close the park down. Really , it was only worthwhile because we were all still awake, energetic, and MK was the only park still open past 9pm. The next day, we had to sleep in a little.