This is exactly what my family is doing. We have a Disney VISA so we booked on Monday. We had reservations already, but changed them to take advantage of
Free Dining.
I now have two reservations. The first is a three night room-only reservation for the nights of August 21-23. We were lucky enough to get a PIN code for 30% off the rack rate for our resort (Coronado Springs), and we were allowed to keep the savings on that separate first reservation.
Then, we booked seven nights under a separate reservation (August 24 -30) on the Free Dining plan. So, starting August 24 we have the free dining, but we are paying the value season rack rate for the room - no 30% off.
The main problem with doing it this way is you need to buy at least a one-day Magic Your Way ticket with the Free Dining reservation. For us, that means we will be ticketless until the morning of August 24, unless we buy another set of tickets, which isn't very economical. Our solution - spend August 21 (our travel day) at the resort pool, spend August 22 at a water park (which won't be included anyway on our MYW tickets), and then spend August 23 in Downtown Disney. We'll get our Park Hopper tickets on the morning of the 24th, and away we go!!
I've read that others in our situation have purchased the one-day MYW ticket with the Free Dining plan, and then separately purchased MYW tickets to cover their entire stay. They have said they'll use the Free Dining, and then simply keep the one-day park ticket to use on a later vacation. We're not certain when our next Disney vacation might be, so this isn't going to work for us.
Either way, if you have two reservations, you will need to technically check-out and check back in on the morning of the 24th (along with hundreds of others no doubt, so come early). But based on info I've seen in other posts, it sounds like it's very doubtful that you would have to actually change rooms (although that's not guaranteed).
Whether it's worth doing I guess depends on how long you're staying after the 24th. But the dining plan, if you purchase it, costs around $39/day for adults and juniors (11 and over) and $11/day for kids under 11. So, you're talking pretty big savings potentially, especially if you like to dine at some of the higher-priced restaurants. It was certainly enough for us to give up our 30% off discount on the room
Anyway, it's very much allowed to make seperate reservations like this. I handled both reservations on one call with a Disney CSR. Good luck!