Yes, with exceptions.
- The OS from the 2010 MBP cannot be older than the one that the 2011 MBP initially shipped with.
- The HDD will have the network configuration of the 2010 MBP and if you run it, un-modified, on the same network as the 2011 MBP, you may have conflicts. I ran into this problem with the computer name and found that the typical ways to re-name the computer didn't work (it wanted to use the old name) and I had to edit one of the configuration files (can't remember which one) to make it work. I haven't investigated that deeply into the issue but you should probably be sure that the other computer with the same name isn't running, rename the computer to something different, restart to make sure the new name has taken hold and then try running the other computer. I was doing this as a test so maybe if you do some research, there's a better way to handle this or maybe somebody on the forum will respond with a better way to handle this. Or, because I use a static IP address vs. DHCP, maybe that's the issue. Also, if you configured the router specifically to the IP address or MAC address of the old computer, then that has to be taken into account.
- If you have any programs or cloud services that use the MAC (media access control) address or the serial number of the old computer, then there may be an issue there. I think software protection keys rely on one or the other so if you have software like that, it won't run. I think I've read that some of the Apple cloud services rely on the MAC address for identification, but that's another issue I haven't researched since I don't use any of the Apple cloud services.