Your old drive would probably NOT be able to boot your new laptop successfully. Laptops are notoriously picky about drivers and such. Acronis should be able to restore your backup to a new partition on your new laptop, but you would have to install any of your old programs in order to get them to work. there need to be entries in the registry for your programs to work correctly.
Thanks for taking the time to answer clarkjd, I appreciate it. It's not the good news I was hoping for but it's better than proceeding under false expectations.