Running Battlefield 2142 on two computers with one Origin account?

(This is a question about Battlefield 2142, not Battlefield 3 as the product selected says. They didn't give an option for 2142!)

We have two laptops at home. I just bought Battlefield 2142 Deluxe through Origin, and it is installed on one computer. If I install it on the other computer, will both computers be able to run it (and particularly play together in multiplayer) simultaneously? Please note that I tried the same thing with the 2142 CD download purchased from a retail store, and we couldn't run Battlefield 2142 on both computers at the same time. This was because of the need to log in with an account and only one account being able to be registered with the CD product key/serial number. The single account wouldn't be playable on both computers simultaneously, as one would log out as the other logged in. And, to restate, a second account couldn't be created on a second computer that had had the program installed with the same CD and product code as the first computer. Would this issue come up if I download 2142 on both computers through the same Origin account?
Sorry if I didn't make much sense. Please let me know if I need to clarify any further! Any help is much appreciated!!