Absolutely. Just use desktop manager to load the backed up file onto the new device. If I remember correctly, anything that isn't compatible won't be loaded. All your contacts and calendar entries should transfer with no issue. Sorry to hear you lost your phone.
Just don't do with an os change and third party apps. I got a new storm the other day and upgraded to .151 and added my third party apps in (which are pin specific) and bricked my storm. If all your doin is restoring from DM your fine.
It's a brand new phone (or refurb)? Personally I would take a week to break in the new device with the default OS, just to make sure there aren't any issues with the device. You could load your contacts and what not, skipping to reload any third party data in the backed up file. Then if all is well, you could reload 7.1, and the rest of your stuff. My thought is having to go through the trouble of loading 7.1, then realizing there's an issue but you don't know if it's from the device or the OS.