Yes, you would get all the promotions if you qualified as a new customer. You would still be without TV for 3 months so the customer would have to decide which is more important.
If available in your area, why not sign up for cable for a few months to fill the gap? I noticed the cable company that operates in my area offers 6-month new customer promos with no contract. So, when you are eligible and ready to go back to Dish and collect your new equipment and new customer promotions, you could drop cable at that time, or maybe you'd find you like cable better and want to stick with it, or stick with cable for at least the full six discounted months, thus collecting 18 months of consecutive discounted service (6 months cable plus 12 months Dish).
People jump all over me for saying stuff like this, but I see no ethical problem with accepting promotions that are offered by companies. You're not lying about anything. They're offering new customer promotions, you're a new customer. If providers don't like that type of behavior, they can always start offering loyalty bonuses instead or in addition to new customer promos. You said yourself, you'd be happy to stick with Dish in the first place if they'd just give you the same equipment upgrades a new customer gets.
I also personally won't feel guilty if I switch from Dish to cable at some point to get new customer and bundling discounts and then came back. Dish made me pay for installation and only offered SD equipment even though their stated promo at the time was free installation and free HD for life. If I left and then came back, maybe they'd do what they should have done in the first place, and I'll mentally apply my new customer discount to the fee I had to pay the first time.
Or maybe I'd just stick with cable or go to Directv. All these companies have issues- I had a long saga with the cable company that turned into an article on the Consumerist. I'm not advocating one over the other. I'm just saying it makes sense to get the best deals you can.
Of course, here I am well beyond my contract and still with Dish, so maybe I'm more loyal than I let on.
Inertia is a powerful thing, and Dish does offer me a key channel that cable doesn't. But I think when my two year cable Internet promotional rate expires in a month or two, I'm going to have to bring down total cost, and switching TV providers and getting a new customer and bundling discount seems like the way to do it short-term. Then Dish or Directv can try to lure me back. And if they don't offer me HD equipment and such this time, they won't get me a second time. The first time, I was desperate, but I never really like the way they shortchanged me and it sticks in my craw years later. People remember this stuff. I remember it every time I see one of those stupid downgraded HD to SD signals that has bars on all four corners of the screen where even stretching it leaves one set of bars and it turns watching hockey into almost total guesswork if your RSN has blurry cameras to begin with.