My Xbox 360 broke one day while I was not connected to Xbox Live. I recovered my Gamertag on my friend's Xbox 360 while connected to Xbox Live. I then earned a couple of achievements on his Xbox 360 while online.
Later on, I got a new Xbox 360 and started earning other achievements at home (note: still not connected to Xbox Live at this point). If I signed into Xbox Live and tried to recover my Gamertag back on my Xbox 360, would I still have the achievements I earned on my friend's Xbox 360 in addition to the ones that I just earned on my new offline Xbox 360 account?